While driving from A-ville to B-town, Harriet drove at a constant spee

Question

While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

A. 138
B. 148
C. 150
D. 162
E. 168

Kudos for a correct solution.

A. 138
B. 148
C. 150
D. 162
E. 168

Kudos for a correct  solution .

Bunuel · Accepted Answer

MAGOOSH OFFICIAL SOLUTION harriettakestrip_text.PNG

Celestial09 · Answer

Its D.
Here it goes:
Distance will be same both sides... hence total distance will D+D= 2D
Total time given+ 5hrs
Speed per side also given.. 115km/ph and 135 km/ph
Speed= Distanct/Time
D/s1 + D/s2= total time
(d/115) + (d/135) = 5
solving it D comes to 621 km
Hence each side is D/2 : 621/2 = 310.5 km
Time for first journey is 310.5/115 which is 162 mins
Thanks

Kudos please if my solution is correct!

jakeqs · Answer

X = Time from A to B
Y = Time from B to A
X+Y=5 hrs total travel time
115X=135Y since the distances are the same

X+Y=5 => 135X+135Y=675
115X=135Y => 115X-135Y=0 
Combined you get
250X=675 hrs
X=2.7 hrs * 60 mins/hr= 162

LaxAvenger · Answer

Hello,

I have struggles coming from (D/115) + (D/135) = 5
to D = 621

could you explain the calculation steps ?

Celestial09 · Answer

Hello!
Thanks for addressing your doubt. here it goes:
(d/115) + (d/135) = 5 kindly note.. its addition of two fractions... so I kindly take 5 common from both denominators... hence you will be left with d/23 + d/27 and that 5 will cross multiply to other side of equation.. resulting
d/23 + d/27 = 25
then kindly solve it ... 27d +23 d = 25*23*27
d will come down to 310.5
which i particularly took as total distance 310.5*2 = 621 km
hope it makes sense.
thanks

PareshGmat · Answer

Answer = D = 162

Let distance between A & B = d

Setting up the time equation

\frac{d}{115} + \frac{d}{135}= 5

d = \frac{23 * 27}{2}  (Need not have to solve)

Time required in minutes from A to B  = \frac{23*27}{2*115} * 60 = 162

rombo27 · Answer

Distance from A to B is the same as distance from B to A. Hence

115x=135y 
x/y=135/115 => x/y=27/23 
so x= 27/50 of the total time (50=27+23).
total time x+y=5h= 300minutes,

x= 300m*(27/50)= 162m

Answer. D

kevinakbaraly · Answer

Hi everyone,

I don't see why we divide the distance 625 by 250 and not 115, while Harriet drives from A to B at 115mph...
Does not make sense to me.

But at the same time, dividing 625 by 115 gives us a time of 5+ hours, which is also impossible because the whole trip A --> B --> A takes 5 hours.
Can someone please give some insights?

Many thanks in advance

jurin · Answer

5hr = 300min. 
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.

Now let plug in ans. D or E and verify which one give same distance on each leg.

D. t= 162min
* leg A-B ---> d = 115.162/60 = 18630/60
* leg B-A ----> d = 135*138/60 = 18630/60

so the correct ans. is  D

lalania1 · Answer

Rates and Distance: Q: Find t on the way in?
When you are given the same distance on the way in and back. ex: d
and you are given the rates for back and forth. ex: 115 and 135
and you are given the total time. ex: 5

step1: organize the formulas like below. Use 5-t for the time on the way back = very important.

rt=d
115 (t) = d
135 (5-t) = d

step2: Make the two equations equal and solve for t

115(t) = 135 (5-t)
t= 27/10 hours

step3: check the convention of time that the question wants you to answer and convert if needed

In this question, you are asked for minutes, so you need to do one more thing before jumping into the answers

27/10 hours * 60minutes = 162 minutes

rohit_arora · Answer

Distance taken = speed*time
Let Harriet took x hrs to go from A to B and y hrs to come from B to A.
 Distance=115*x=135*y 
 x+y=5 (total time=5 hrs.) 
we need to find x.
 y=5-x 
Substituting in Distance equation.
 115*x=135(5-x)
Solve to get x=2.7hrs
2.7*60=162mins.
Answer=D.

Thanks. Please give   KUDOS   if correct.

gracie · Answer

average speed for round trip≈125 kph
125*5=625 round trip miles
625/2=312.5 one way miles
312.5/115=2.72 hours
2.72*60=163.2 minutes
closest to 162
D

yezz · Answer

distance travelled is the same in each direction thus time is inversely proportional to speed , total time = 5 , let first leg time t and 2nd leg time = 5-t

115/135 = 5-t / t thus , t in hours = 5*27/50 , in minutes = 300*27/50 = 6*27 = 162..........D

Mahmud6 · Answer

I solved in following way;

Rate of driving from A-ville to B-town is 115 kmph
Rate of driving from B-town to A-ville is 135 kmph
Therefore, the ratio of rate is 115:135

Since the distance is same, the ratio of time would be reciprocal of ratio of rate.

So, ratio of time would be  135:115=27:23; 27x:23x

Total time taken is 5 hours=300 minutes

27x+23x=50x

Given,  50x=300 
 x=6

So, time taken to drive from A-ville to B-town would be  27x=27*6=162

rahul16singh28 · Answer

Let the time from A to B be t1 and time from B to A be t2.

t1 + t2 = 5

115*t1 = 135*t2  -->  t2 = \frac{23}{27}t1 
 t1 = 2.7 Hours.

manjot123 · Answer

why make equations
since distance is same 
speed will be inversely propotional to time
s1 : s2 
115: 135
t1:t2
135:115
27:23
27/50(5*60) = 162 mins

ScottTargetTestPrep · Answer

Solution:

We can create the equation where t is the number of hours it takes Harriet to drive from A-ville to B-town:

115t = 135(5 - t)

115t = 675 - 135t

250t = 675

t = 675/250 = 2.7

So it takes 2.7 hours or 2.7 x 60 = 162 minutes for Harriet to drive from A-ville to B-town.

Answer: D

ranand06 · Answer

Sr1994 · Answer

if the distance is the same, we can use   S1T1=S2T2

Here, S1= 115km/hr
S2= 135km/hr
T1+T2 = 5hrs

T2= 5-T1

115T1 = 135(5-T1)
115T1 = 675 - 135T1
250T1 = 675

T1 = 2.7hrs
Multiply with 60 to convert hours into minutes.

2.7*60 = 162 minutes
 Answer : D

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