Question

If a person walks at 4 mph, he covers a certain distance. If he walks at 9 mph, he covers 8.5 miles more. How much distance did he actually cover?
A) 5.5 miles
B) 6.8 miles
C) 7.8 miles
D) 8 miles

Answer 1

Hint: If a person walks at different speeds for an equal interval of time. The distance covered will be more when speed is more and time is constant. In both cases, time traveled is the same. The formula of distance is, $d = s \times t$ where d is the distance, s is the speed and t is the time taken to travel.

Complete step-by-step answer:
Given, the person walks at 4mph
Let the time be x hrs
We know that $d = s \times t$ where d is the distance, s is speed, and t is time.
So, to calculate distance, we will multiply speed with the time taken.
Therefore, Distance,$d = 4x$
When the person walks at 9mph
Let the time be x hrs
We know that $d = s \times t$ where d is the distance, s is speed, and t is time.
So, to calculate distance, we will multiply speed with the time taken.
Because time is equal in both the cases.
${d_1} = 9x$
The person walking with the speed of 9mph covers 8.5miles more
Therefore, ${d_1} = d + 8.5$
Now equating both the equation,
$ \Rightarrow 9x = 4x + 8.5$
on solving this,
$\
   \Rightarrow 5x = 8.5 \\
   \Rightarrow x = 1.7
$
So, the time is $1.7$ hours
Now for 4mph, distance is
 $d = 4 \times 1.7 = 6.8miles$
Hence, the distance he actually covers is 6.8 miles.

The answer to this question is Option (B) 6.8 miles.

Note: The question can also ask what is the distance covered when the speed is 9mph.
And for 9mph, distance is the product of speed i.e., 9mph and the time we calculated in the above question is 1.7 hrs.
Therefore,
${d_1} = 9 \times 1.7 = 15.3miles$