Question

A man and a woman 81 miles apart from each other start travelling towards each other at the same time. If the man covers 5 miles/hour compared to woman’s 4 miles/hour, how far will the woman have travelled when they meet?
A.27
B.36
C.45
D.32

Answer 1

Hint: Suppose after x hours they meet. Then, as the speed of man was 5 miles/hour then, we can say after x hours distance travelled by him is 5x. As the speed of the woman was 4 miles/hour then, we can say after x hours distance will be 4x. Now, as they met, we can say \[5x + 4x = 81\], hence, find x. And to find distance travelled by woman is 4x, so finally find it.

Complete step-by-step answer:
In the question, we are told that a man and a woman are 81 miles apart from each other and they are starting to travel towards each other at the same time. It is further said that a man completes or covers 5 miles an hour compared to that of a woman who completes or covers 4 miles an hour. Thus, when they meet we have to find the distance covered by the woman.
So, it is said that both man and woman reached each other at some point. Let's say they reached by x hours.
As the man covers 5 miles per hour then, after x hours the distance travelled by the man will be \[5{\rm{ miles/hour }} \times {\rm{ x hours }} \Rightarrow {\rm{ 5x miles}}{\rm{.}}\]
As for the woman, who covers 4 miles per hour then, after x hours the distance travelled by the woman will be \[{\rm{4 miles/hour }} \times {\rm{ x hours }} \Rightarrow {\rm{ 4x miles}}{\rm{.}}\]
We know that, after x hours both man and woman meet. So, we can say after x hours the sum of the distance travelled by both is 81 miles.
Hence, from this we can say that,
\[\begin{array}{l}5x + 4x = 81\\ \Rightarrow 9x = 81\\ \Rightarrow x = \dfrac{{81}}{9}\\ \Rightarrow x = 9\end{array}\]
Hence, the value of x is 9.
We have to find the value of 4x as it is asked, what is the distance travelled by a woman.
Thus, value of x is 9, hence, value of 4x will be \[4 \times 9 \Rightarrow 36{\rm{ miles}}{\rm{.}}\]
Thus, the correct option is B.

Note: If the speed of man and woman are given as 5 miles/hour and 4 miles/hour and they are moving towards each other in opposite direction on the road which is of 81 miles, so, one can find the time of meet by using formula \[\dfrac{{{\rm{Distance}}}}{{{\rm{Sum \ of \ the \ speed}}}}\].
If they would have been travelling in same direction then, the time of meet would be \[\dfrac{{{\rm{Distance}}}}{{{\rm{Difference \ of \ the \ speed}}}}\].