Question

Determine the rate of change: Jim and John were traveling in separate cars from LA to NYC. Jim's speedometer was broken and had to follow John the entire trip. They drove 100 miles in 1.75 hours and stopped for lunch. They then travelled 150 miles in 157.5 minutes before stopping for the day. (Round to the nearest 100th)

Answer 1

The rate of change of distance with time is given by dividing the distance

covered with time taken to cover the distance.

The average rate of change of the distance with time is 57.14 mph.

Reason:

The distance travelled in the first 1.75 hours  = 100 miles

The distance travelled in the next 157.5 minutes = 150 miles

157.5 minutes = $\frac{157.5}{60}$ hours

The average rate of change of distance with time is therefore;

$Average \ rate \ of \ change \ of \ distance \ with \ time = \dfrac{100 + 150}{1.75 + \dfrac{157.5}{60} } = \dfrac{400}{7} = 57\frac{1}{7}$

The average rate of change of distance with time is $57\frac{1}{7}$ mph ≈ 57.14 mph.

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