Two buses, P and Q, started simultaneously from opposite ends of a 140

Question

Two buses, P and Q, started simultaneously from opposite ends of a 140 mile route and travelled towards each other on parallel roads. Bus P, travelling at a constant rate, completed the 140 mile trip in 9 hours and Bus Q, travelling at constant speed, completed the 140 mile trip in 5 hours. How many miles had Bus P travelled when it first met Bus Q.

A. 50
B. 60
C. 70
D. 90
E. 100

A. 50
B. 60
C. 70
D. 90
E. 100

bv8562 · Accepted Answer

Speed = Distance/Time

Speed (Bus P) = 140/9

Speed (Bus P) = 140/5

Relative Speed: Total Time = Distance b/w them/(Sum of speeds) = 140/(140/9+140/5) = 45/14 hrs

Distance travelled by Bus P in 45/14 hrs = 140/9*45/14 = 50 kms (A)

Bunuel · Answer

Copy of the following OG question: https://gmatclub.com/forum/two-trains-x ... fl=similar

Scuven · Answer

Total space =140

Speed of P =140/9 which can be approximated as (140/10) = 14
Speed of Q = 140/5= 28

Relative speed (sum since they are going in opposite direction) =14+28=42
Space to cover =140

Relative Time = Space/Relative speed = 140/42 =approximately 3 (time P and Q encounter each other)

For t=3 calculate Space travelled by P

Thus space= speed * relative time = 14 *3 =42 (approximate) (distance travelled by P when it encounters Q)

Since we approximated the speed of Q by increasing the denominator to 10 the overall result is underestimated, it should be a little more that 14
In addition we estimated T=3 but it should be a little more than 3

Thus the product 14*3 should be higher and the closed answer is A

btsaami · Answer

Method 1: Time required to meet, t = 140/(140/9+140/5)
t=45/14 hours

Distance travelled by P= 140/9 * 45/14
= 50 km

Method 2: Time at which they meet is constant. Hence, 
Dp/Sp= Dq/Sq
Sp/Sq= Dp/Dq.

Let x be the distance travelled by P.
(140/9)/(140/5)= x/(140-x)
5/9=x/(140-x)
Solve for x or check from options.
x=50 km

Two buses, P and Q, started simultaneously from opposite ends of a 140

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Two buses, P and Q, started simultaneously from opposite ends of a 140

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