Question

Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:

(a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much

Answer 1

Hello !
Let the time spent in covering 50 be t sec.
let the speed for the first trip be s=50/t
⇒t=50/s              ...........................     1.
The speed for the 300 mile trip = 3×s = 3s
Let the time be t1
so , 
3s = 300/t1 
t1=300/3s = 100/s      .......................     2.
Now, 
Comparing the both time we will get,
t1/t = (100/s) / ( 50/s)
t1/t = 100 ×s / 50 ×s 
t1 / t = 100/50
t1 / t = 2/1  .....................   3
⇒ 2×t = t1                                          Ans.

So the correct option is (b).
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Answer 2

Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.

We know that

Speed = Distance/Time.

So,

Time = Distance/Speed.

So,

Time Taken to Cover a Distance of 50 miles on his First Trip = 50/x hr.

And Time Taken to Covered a Distance of 300 miles on his later trip = 300/3x hr.

= 100/x hr.

So,

Time Taken Later is Twice As before Time Taken

So,

ANSWER = (b) = Twice as Much

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