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piyush272
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Sanjana jogged uphill for a while at an average speed of 3 06 Oct 2013, 04:41
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Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

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my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2
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D
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kusena
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Sanjana jogged uphill for a while at an average speed of 3 06 Oct 2013, 05:09
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piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

a. 1 mile
b. 1 1/3 miles
c. 1 1/2 miles
d. 1 3/5 miles
e. 1 2/3 miles

my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2

Let the uphill distance be D1 with speed S1=3miles/hr and downhill distance be D2 with speed 8 miles/hr

D1/3+D2/8=40/60 hrs
=>8D1+3D2=16------Eq(1)

also given she travelled uphill and downhill at an avg of 4 miles/hr
=>total distance/Avg speed=40/60hrs
=>(D1+D2)/4=2/3
=>3D1+3D2=8-------Eq(2)
solving equations 1 and 2
D1=8/5 mile and D2=16/15 miles
=>D1=1 3/5 miles

the formula for average speed s1*s2/s1+s2........can be used only when uphill distance and downhill distances are same which is not in this case..

Hope it is helpful
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Sanjana jogged uphill for a while at an average speed of 3 31 Dec 2013, 12:15
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piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2

Easy question

3x + 8y / x+y = 4
x + y = 40

So solving y = 8
x = 32

So D is out correct answer choice

Hope it helps
Provide kudos!

Cheers
J :)
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Sanjana jogged uphill for a while at an average speed of 3 26 Nov 2013, 17:02
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kusena
piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

a. 1 mile
b. 1 1/3 miles
c. 1 1/2 miles
d. 1 3/5 miles
e. 1 2/3 miles

my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2

Let the uphill distance be D1 with speed S1=3miles/hr and downhill distance be D2 with speed 8 miles/hr

D1/3+D2/8=40/60 hrs
=>8D1+3D2=16------Eq(1)

also given she travelled uphill and downhill at an avg of 4 miles/hr
=>total distance/Avg speed=40/60hrs
=>(D1+D2)/4=2/3
=>3D1+3D2=8-------Eq(2)
solving equations 1 and 2
D1=8/5 mile and D2=16/15 miles
=>D1=1 3/5 miles

the formula for average speed s1*s2/s1+s2........can be used only when uphill distance and downhill distances are same which is not in this case..

Hope it is helpful

But aren't the uphill and downhill distances actually the same?
Are we assuming is the same hill no?

Cheers
J :)
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Sanjana jogged uphill for a while at an average speed of 3 27 Nov 2013, 00:45
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jlgdr
kusena
piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

a. 1 mile
b. 1 1/3 miles
c. 1 1/2 miles
d. 1 3/5 miles
e. 1 2/3 miles

my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2

Let the uphill distance be D1 with speed S1=3miles/hr and downhill distance be D2 with speed 8 miles/hr

D1/3+D2/8=40/60 hrs
=>8D1+3D2=16------Eq(1)

also given she travelled uphill and downhill at an avg of 4 miles/hr
=>total distance/Avg speed=40/60hrs
=>(D1+D2)/4=2/3
=>3D1+3D2=8-------Eq(2)
solving equations 1 and 2
D1=8/5 mile and D2=16/15 miles
=>D1=1 3/5 miles

the formula for average speed s1*s2/s1+s2........can be used only when uphill distance and downhill distances are same which is not in this case..

Hope it is helpful

But aren't the uphill and downhill distances actually the same?
Are we assuming is the same hill no?

Cheers
J :)

Question says average speed of both the journeys is 4 miles/hr
Where as uphill speed 3miles/hr and downhill speed 8 miles/hr
If both uphill and down hill distances are same then the avg speed will be (v1*v2)/(v1+v2)=8*3/(8+3)=24/11 miles/hr
which is not equal to 4 miles/hr.hence the the distances traveled uphill and downhill aren't the same.
Hope its clear
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Sanjana jogged uphill for a while at an average speed of 3 14 Feb 2014, 13:57
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piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2

Easy question

3x + 8y / x+y = 4
x + y = 40

So solving y = 8
x = 32

So D is out correct answer choice

Hope it helps
Provide kudos!

Cheers
J :)

Just found another way of doing it with weighted average.

Let's call x the uphill distance and y the downhill distance

Also we know that average speed is 4mph.

So x is at 3mph and y is at 8mph. By differentials

x = 4y. So if total time is 40 minutes then the time spent uphill must be 4 times that spend downhill

Therefore x = 32 min. Now, (3)(32/60)=1 3/5

Hope you enjoyed
Cheers
J
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Sanjana jogged uphill for a while at an average speed of 3 03 Oct 2015, 01:15
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add times to get 2/3 hours (40min.) and consider full distance (2/3)*4=8/3:

x/3 + (8/3)-x)/8=2/3

5x=8

x=8/5 => 1+3/5

D
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Sanjana jogged uphill for a while at an average speed of 3 03 Oct 2015, 15:08
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let D=uphill distance
D/3 hours=uphill time
(4 mph avge speed)(2/3 hour total time)=8/3 miles total distance
8/3-D=downhill miles
(8/3-D)/8=downhill time
D/3+(8/3-D)/8=2/3
D=8/5➡1+3/5 miles
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Sanjana jogged uphill for a while at an average speed of 3 04 Mar 2016, 19:14
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i used only 1 variable to solve this question...
uphill 3mph - time 2/3-x - distance 2-3x
downhill 8mph - time x - distance 8x

total distance 8/3 miles

so 2-3x+8x=8/3
5x=8/3 - 6/3
5x = 2/3
x=2/15

now, distance uphill is 2-3x
2-2/5 = 1 and 3/5

D
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Sanjana jogged uphill for a while at an average speed of 3 19 Dec 2016, 11:18
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Apply mixture and alligation method.
Please refer the attached diagram.
time spent at the rate of 3 miles/hr: time spent at the rate of 8 miles/hr = 4:1
So reqd time = 4/5*40 = 32 minutes

So distance traveled = 32/60 * 3 = 8/5 = 1 3/5 miles.
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Sanjana jogged uphill for a while at an average speed of 3 21 Jul 2017, 20:10
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D=Distance
R=Rate
T=Time
T1= Time 1 = Uphill
T2 = Time 2 = Downtown
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Sanjana jogged uphill for a while at an average speed of 3 16 Dec 2018, 14:25
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piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

Let's start with a "Word Equation"
(distance traveled uphill) + (distance traveled downhill) = TOTAL DISTANCE

Let t = the time spent jogging UPHILL (in hours)
The total travel time = 40 minutes = 2/3 HOURS
So, 2/3 - t = the time spent jogging DOWNHILL (in hours)

Distance = (speed)(time)
So, we can rewrite our word equation as: 3t + 8(2/3 - t) = (4)(2/3)
Expand to get: 3t + 16/3 - 8t = 8/3
Subtract 16/3 from both sides to get: 3t - 8t = -8/3
Simplify to get: -5t = -8/3
Solve: t = (-8/3)/(-5) = 8/15
So, Sanjana spent 8/15 hours traveling UPHILL

How far did Sanjana jog uphill?
Distance = (speed)(time)
So distance = (3)(8/15) = 8/5 = 1 3/5 miles

Answer: D

Cheers,
Brent
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Sanjana jogged uphill for a while at an average speed of 3 10 Mar 2019, 20:06
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piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

We can let t = the number of hours Sanjana jogged uphill. Since 40 minutes = 2/3 of an hour, the time she jogged downhill was (2/3 - t) hours. We can create the equation:

3t + 8(2/3 - t) = 4(2/3)

3t + 16/3 - 8t = 8/3

-5t = -8/3

t = 8/15

Since she jogged 8/15 of an hour uphill at an average speed of 3 mph, she jogged 8/15 x 3 = 8/5 = 1 3/5 miles.

Answer: D
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Sanjana jogged uphill for a while at an average speed of 3 30 Jun 2023, 23:18
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[quote="piyush272"]Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles


one thing that i can't understand is how upward and downward distance are different? if u r moving up with d distance then you have to move down d distance
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Sanjana jogged uphill for a while at an average speed of 3 12 Oct 2023, 01:54
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Why uphill and downhill distance are different?

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Sanjana jogged uphill for a while at an average speed of 3 12 Oct 2023, 02:01
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Why uphill and downhill distance are different?

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Please review the highlighted portion of the question. Then, revisit the solutions above with that specific section in mind.

Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?
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Sanjana jogged uphill for a while at an average speed of 3 16 Jan 2024, 09:35
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piyush272
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

Show Spoiler
my question is in such problems why cant we use the formula for average speed s1*s2/s1+s2

Let time to travel uphill=u minutes, downhill=d mins.
equation 1: (3u+8d)/(u+d)=4 or, u=4d.
equation 2: u+d=40.
Solving both equations, we get d=8 and u=32.
If in 60 minutes, Sanjana goes 3 miles.. then in 32 minutes - (3*32)/60=1 3/5(D)
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Sanjana jogged uphill for a while at an average speed of 3 19 Jan 2025, 00:45
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