Question

Beth drives 200 miles in 4 hours. She drives the first 18 miles at an average speed of 36 mph. Work out her average speed for the rest of the journey...

Answer 1

Beth travelled the remaining distance with an average speed of 52 mph

Solution:

Given, Beth drives 200 miles in 4 hours.  

The formula for distance speed is given as:

$\text { distance }=\text { speed } \times \text { time. }$   --- eqn 1

Calculating time taken for 18 miles:

She drives the first 18 miles at an average speed of 36 mph.  

Here distance = 18 miles

speed = 36 mph

Plugging in values in eqn 1 we get,

$\begin{array}{l}{\rightarrow 18 \text { miles }=36 \mathrm{mph} \times \text { time }} \\\\ {\rightarrow \text { time }=\frac{1}{2} \text { hour }}\end{array}$

Calculating average speed for the rest of the journey:

Now, remaining distance = 200 miles – 18 miles = 182 miles

And time used for remaining journey = total time – time taken for first 18 miles

$4 \text { hours }-\frac{1}{2} \text { hours }=\frac{7}{2} \text { hours }$

Plugging in values in eqn 1, we get

$\begin{array}{l}{182 \text { miles }=\text { average speed } \times \frac{7}{2} \text { hours }} \\\\ {\text { Average speed }=\frac{182}{7} \times 2=52}\end{array}$

Thus the average speed for rest of journey is 52 mph