Question

One plane travels at 600 miles per hour and the other at 720 miles per hour. Find the difference between the distances covered in 12 seconds by the two planes.
A. $ \dfrac{1}{{30}} $
B. $ \dfrac{2}{5} $
C. 2
D. 30

Answer 1

Hint: The speeds of the two planes are given in miles/ hour. And the difference of the distances is asked for 12 seconds. So first convert their speeds into miles/ seconds and then multiply the obtained speeds by 12 seconds to get the distance travelled in 12 seconds by both the planes. And then find their difference by subtracting the smaller value from the larger value.

Complete step-by-step answer:
We are given that one plane travels at 600 miles per hour and the other at 720 miles per hour.
We have to find the difference between the distances covered in 12 seconds by the two planes.
1 hour has 60 minutes and 1 minute has 60 seconds.
This means 1 hour has $ 60 \times 60 = 3600 $ seconds.
Therefore, 600 miles per hour means
$\Rightarrow \dfrac{{600}}{{3600}} = \dfrac{1}{6} $ miles per second
And,720 miles per hour means
$\Rightarrow \dfrac{{720}}{{3600}} = \dfrac{1}{5} $ miles per second
First plane travels at a speed of $ \dfrac{1}{6} $ miles per second and the second plane travels at a speed of $ \dfrac{1}{5} $ miles per second.
Distance is the product of speed and time.
Distance traveled by the first plane in 12 seconds is
$\Rightarrow {d_1} = \dfrac{1}{6} \times 12 = 2 $ miles.
Distance traveled by the second plane in 12 seconds is
$\Rightarrow {d_2} = \dfrac{1}{5} \times 12 = \dfrac{{12}}{5} $ miles.
As we can see $ {d_2} $ is greater than $ {d_1} $ . So subtract $ {d_1} $ from $ {d_2} $ .
Difference in distances is
$\Rightarrow {d_2} - {d_1} = \dfrac{{12}}{5} - 2 = \dfrac{{12 - 10}}{5} = \dfrac{2}{5} $ miles.
So, the correct answer is “Option B”.

Note: Here to find the difference in distances we have subtracted the smaller distance from the larger distance, because the distance will never be negative and we have to get a positive result. So only when subtracting smaller one from larger one, we will get a positive result.