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...

Beth travelled the remaining distance with an average speed of 52 mphSolution:Given, Beth drives 200 miles in 4 hours.  The formula for distance speed is given as:[tex]\text { distance }=\text { speed } \times \text { time. }[/tex]   --- eqn 1Calculating time taken for 18 miles:She drives the first 18 miles at an average speed of 36 mph.  Here distance = 18 milesspeed = 36 mphPlugging in values in eqn 1 we get,[tex]\begin{array}{l}{\rightarrow 18 \text { miles }=36 \mathrm{mph} \times \text { time }} \\\\ {\rightarrow \text { time }=\frac{1}{2} \text { hour }}\end{array}[/tex]Calculating average speed for the rest of the journey:Now, remaining distance = 200 miles – 18 miles = 182 milesAnd time used for remaining journey = total time – time taken for first 18 miles[tex]4 \text { hours }-\frac{1}{2} \text { hours }=\frac{7}{2} \text { hours }[/tex]Plugging in values in eqn 1, we get[tex]\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}[/tex]Thus the average speed for rest of journey is 52 mph