The distance between two cities, A and B, is 900 miles. A bus starts

Question

The distance between two cities, A and B, is 900 miles. A bus starts from A for B at 7:00 am. Another bus starts from B for A at 8:30 am. What is the speed of the first bus?

(1) The speed of the second bus is 4/7 of the speed of the first bus.
(2) The two buses cross each other at 7:00 pm on the same day.

GMATinsight · Accepted Answer

Speed = \frac{Distance}{Time}

Question : Speed of first bus = ?

Statement 1 :Ratio of speeds of first and second bus = 7/4 
since we don't know the time of their meeting on the way hence we can not figure out what their exact speeds are. There will be multiple solutions with the same ratio of speeds
NOT SUFFICIENT

Statement 2 :The two buses cross each other at 7:00 pm on the same day 
Now, we know the meeting time of the buses but their ratio of speeds is known hence
NOT SUFFICIENT

Combining the two statements  
We know the ratio of speeds and also the travel time of each bus hence we will know what are the speeds respectively
i.e. Time taken by first bus to travel the distance = 12 hours  speed  7x
i.e. Time taken by Second bus to travel the distance = 10.5 hours  speed  4x
Total Distance travelled = 900

900 = 7x*12+10.5*4x
Which gives us x and thereby gives us the speed

SUFFICIENT

Answer: option C

abhishek911 · Answer

Here's my solution. But it took me around 3 mins with this. Hoping for a better one to be posted by some experts.

From the question :

First, let d1 be the distance covered by bus A in 1.5 hours (bw 7-8:30 AM)

Also,  d1 = 1.5*S_a 
Total time the two buses travel together till they meet= T

Let  S_a  be the speed of bus A and  S_b  be the speed of bus B.

Using the concept of relative speed, we can say that the distance of 900- d1 is travelled
over a time period of T with a speed of  S_a-S_b

we get  (900 - d1)/T = S_a - S_b

From (1)  
We have,  S_b=(4/7)*S_a

--->  (900 - d1)/T = -(3/7)*S_a

This equation has two variables T and  S_a , hence (1) is not sufficient

From (2)

T = 10.5 hours ( from 8:30 AM till 7 PM)

Again, we get an equation with two variables  S_a  and  S_b

therefore, (2) is not sufficient

But if we combine (1) and (2), we get an equation with one variable, and hence we can find  S_a

Therefore answer is C.

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

The distance between the two cities, A and B, is 900 miles.

A bus, lets say F, travelling at f miles per hour starts from A for B at 7 am.

Another bus, lets say S, travelling at s miles per hour starts from B for A at 8:30 am.

Therefore, F has travelled alone at its own speed for an hour and a half.
Distance covered by F in this time = f * ( \frac{3}{2} ) miles.

We have to find out the value of f.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  The speed of the second bus is 4/7 of the speed of the first bus.

This means, s =  \frac{4 }{ 7}  f; in other words, f = ( \frac{7 }{ 4} ) * s

Unless we have the value of s, we cannot find the value of f.

The data in statement 1 is insufficient to find a unique value for f.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:  The two buses cross each other at 7:00 pm on the same day.

Since bus S started at 8:30 am, the two buses travelled a total distance of (900 –  \frac{3}{2}  f) miles in 10.5 hours and crossed each other at 7 pm.

In case of relative speed questions,

Time taken to meet or cross each other =  \frac{Distance between the objects }{ Relative speed} .

Substituting the values of time and distance between the objects in the equation above, we can find out relative speed. 
However, since the relative speed is the sum of the speeds in this case, we will not be able to find out the value of the individual speeds.

The data in statement 2 is insufficient to find a unique value for f.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1:  The speed of the second bus is 4/7 of the speed of the first bus.
 From statement 2:  The two buses cross each other at 7:00 pm on the same day.

From statement 1, f = ( \frac{7}{4} ) s.

Therefore, relative speed = f + s =  \frac{11 }{4}  s

From statement 2, time taken to cross = 10.5 hours

Distance between the objects = 900 – ( \frac{3}{2} ) f = 900 – ( \frac{3}{2} ) ( \frac{7}{4} )s = 900 – ( \frac{21}{8} )s.

The above values can be substituted into the equation,

Time taken to meet or cross each other =  \frac{Distance between the objects }{ Relative speed} .

Upon doing so, it can be seen that it’s an equation in one unknown, s. The equation can be solved for s and using the value of s, the value of f can be calculated.

The combination of statements is sufficient to find the value of f.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.

The correct answer option is C.

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The distance between two cities, A and B, is 900 miles. A bus starts

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