Question

Car A is 20 miles behind car B, which is travelling in the same direction along the same route as CarA. Car A is travelling at a constant speed of 58 miles per hour and Car B is travelling at a constant speed of 50 miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
$
  (a){\text{ 1}}{\text{.5}} \\
  (b){\text{ 2}}{\text{.0}} \\
  (c){\text{ 2}}{\text{.5}} \\
  (d){\text{ 3}}{\text{.0}} \\
  (e){\text{ 3}}{\text{.5}} \\
 $

Answer 1

Hint – Consider the time taken by Car B to overtake Car A which is travelling ahead of it be t hours. Use the direct relation between distance, speed and time to calculate the time. Now CarB has to travel 20+8 = 28 miles as firstly it is 20 miles behind so it has to cover it and secondly it has to be 8 miles ahead from car A.

Complete step-by-step answer:

Let car A take the time ‘t’ to overtake car B and drive 8 miles ahead of car B.

Now the speed of car A is 58 miles/hr.
And the speed of car B is 50 miles/hr.

Now as we know that the distance, speed and time are related as
Distance = speed $ \times $ time.

So the distance (D1) travelled by car B in time t is
$ \Rightarrow {D_1} = t \times 50$ miles.

Now the distance (D2) travelled by car A in time t is
$ \Rightarrow {D_2} = t \times 58$ miles.

Now it is given that car A is 20 miles behind the car A.

And we have to overtake and drive 8 miles ahead of car B.

So the total distance travelled by car A = (20 + 8) = 28 miles.

So A must cover 28 miles more than B for overtaking 8 miles.

So the difference of distances of car A and car B is 28 miles in that time t.
$ \Rightarrow 58t - 50t = 28$

Now simplify the above equation we have,
$ \Rightarrow 8t = 28$

$ \Rightarrow t = \dfrac{{28}}{8} = 3.5$ hours.

So car A takes 3.5 hours to overtake and drive 8 miles ahead of car B.

Hence option (E) is correct.

Note – In such a type of problem there is more general mathematics involved as compared to formula based, as it uses the constraints of the question to formulate an equation in order to find the variable involved. It is advised to remember the direct formula for distance, speed and time as it saves a lot of time.