Question

Two cars A and B are moving with same speed of $45\,km{h^{ - 1}}$ along the same direction. If a third car C coming from the opposite direction with a speed of $36\,km{h^{ - 1}}$ meets two cars in an interval of 5 minutes, the distance of separation of two cars A and B should be (in km)
A. 6.75
B. 7.25
C. 8.35
D. 4.75

Answer 1

Hint:Since car C is driving in the opposite direction to car A and car B, we can add their speeds and call it relative speed of one car with respect to the other. Use the formula ${\text{speed}}\,{\text{ = }}\,\dfrac{{{\text{distance}}}}{{{\text{time}}}}$ and convert 5 minutes to hours.

Formula used:
${\text{speed}}\,{\text{ = }}\,\dfrac{{{\text{distance}}}}{{{\text{time}}}}$

Complete step by step solution:
Speed of car C relative to cars A and B = $45\,km{h^{ - 1}} + 36\,km{h^{ - 1}} = 81\,km{h^{ - 1}}$
Time taken for car C to go from one car to the other = 5 minutes
Distance = ?
We know that,
${\text{speed}}\,{\text{ = }}\,\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
Therefore,
${\text{distance}}\,{\text{ = }}\,{\text{speed}}\,{{ \times }}\,{\text{time}}$
The units in speed and the units in time are not corresponding. Therefore, we need to change minutes to hours.
5 minutes = $\dfrac{1}{{12}}$ hours
Therefore, time = $\dfrac{1}{{12}}$ hours
Distance = \[81\,km{h^{ - 1}} \times \dfrac{1}{{12}}h\] = 6.75 km

Therefore, the correct option is A.

Note: We need to ensure that we convert 5 minutes to hours so that we can multiply the magnitudes of speed and time to get the magnitude of distance. We can also convert $81\,km{h^{ - 1}}$ to $m{s^{ - 1}}$ and convert 5 minutes to seconds. We will then get the answer in terms of kilometers.