Sanjana jogged uphill for a while at an average speed of 3

Question

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

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

kusena · Accepted Answer

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

jlgdr · Answer

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

jlgdr · Answer

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

kusena · Answer

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

jlgdr · Answer

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

Temurkhon · Answer

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

gracie · Answer

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

mvictor · Answer

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

ganand · Answer

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.

SamBoyle · Answer

D=Distance
R=Rate
T=Time
T1= Time 1 = Uphill
T2 = Time 2 = Downtown

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

pudu · Answer

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

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

Giyo · Answer

Why uphill and downhill distance are different?

Posted from my mobile device

Bunuel · Answer

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?

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

samarpan.g28 · Answer

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

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