A and B start on a journey at the same time. B travels at 4/7th of A's

Question

A and B start on a journey at the same time. B travels at 4/7th of A's rate, and arrives 3 hours 15 minutes after him. How long did each take to complete the whole journey?

A. 91/12 hours, 13/3 hours
B. 89/12 hours, 13/5 hours
C. 91/10 hours, 13/3 hours
D. 91/12 hours, 13/7 hours
E. 91/10 hours, 13/7 hours

Kinshook · Answer

Given: A and B start on a journey at the same time. B travels at 4/7th of A's rate, and arrives 3 hours 15 minutes after him.

Asked: How long did each take to complete the whole journey?

Let the time taken by A = t
D = v1 * t1 = v2 * t2
v1/v2 = t2/t1
4/7 = t / (t + 3.25)
4(t + 3.25) = 7t
4t + 13 = 7t
3t = 13
Time taken by A t = 13/3 hours = 4 1/3 hours
Time taken by B (t+3.25) = 13/3 + 13/4 = 13 * 7/12 = 91/12 hours

IMO A

Akshay J · Answer

Speed A / Speed B = 7/4
 Time A / Time B = 4/7 (Since distance is constant- D = S* T)
Let Time A = 4x
 Time B= 7x
Since B arrives 3 hours 15 mins = 3.25 hours after A
Time B – Time A = 3.25
 7x - 4x = 3.25
 3x= 3.25= 13/4
 x = 13/12
 Time B= 7x = 7 *13/12 = 91/12 hours
 Time A= 4x = 4 *13/12 = 52/12 = 13/3 hours
Option A
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allan89 · Answer

Using product constancy rule, if speed is reduced by n/d then time increases by n/(d-n)

so here speed of B reduces by 3/7, hence time should increase by 3/4

If t is the original time taken by A, then 3/4 * t = 13/4 => t = 13/3 hrs; 
since, B took 13/4 hours more than A, hence B took 13/3 + 13/4 = 91/12 hrs

IMO; product constancy should be the ideal approach for such questions;

ScottTargetTestPrep · Answer

We can let r = A’s rate and t = the time, in hours, it takes for A to complete the journey. Thus, B’s rate = 4r/7, and the time for B to complete the journey is t + 3.25 = t + 13/4 hours. Since they each traveled the same distance, we can create the equation:

rt = 4r/7 (t + 13/4)

rt = 4rt/7 + 13r/7

7rt = 4rt + 13r

7t = 4t + 13

3t = 13

t = 13/3

So A completes the journey in 13/3 hours, and B completes it in 13/3 + 13/4 = 52/12 + 39/12 = 91/12 hours.

Answer: A

TestPrepUnlimited · Answer

By the time A finishes the journey, B still has to travel 3/7ths of the rest of the journey. It took B 3h 15 min to travel the rest of the journey. Hence the full time needed for B is  (3+\frac{1}{4}) / \frac{3}{7} = \frac{13}{4}*\frac{7}{3} = \frac{91}{12} .

Then A's speed is faster so it should be a lower time, thus we multiply by  \frac{4}{7}  to get  \frac{13}{3} .

Ans: A

ZIX · Answer

Or simply you can choose from the options.

(Time taken by A) + 13/4 = (time taken by B)

A. 91/12 hours, 13/3 hours

Here 91/12 + 13/4 = 13/3

vasu1104 · Answer

say rate of A= x k/h
rate of B= 4x/7 k/h
distance is P km

time for A = p/x
time for B = 7p / 4x

now we are given that B reaches after 195 min. lets convert it into hr first. 3 hr + (1/4) hr = 13/4 hr
so basically time difference between two is 13/4

(7p/4x) - (p/x) = 13/4
solving this we get p = 13x/3

we need time for each,
for A, 13/3
for B, 91/12

option A

A and B start on a journey at the same time. B travels at 4/7th of A's

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A and B start on a journey at the same time. B travels at 4/7th of A's

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