Problem
This distance-time graph shows the journey a boat made when it travelled away from a port and then returned.
What was the fastest speed that the boat reached during the journey?
Give your answer in miles per hour and give any decimal answers to 2 d.p.
Solution
Step 1 ：Let $d$ denote the number of miles in the distance from the port and let $r$ denote the fastest speed of the boat (in miles per hour) on the return trip. It takes $d/60$ hours to travel from the port and $d/r$ hours to travel back to the port.
Step 2 ：Round trip, $2d$ miles are covered in $d/60+d/r$ hours for an average speed of \[ \frac{2d}{\frac{d}{60}+\frac{d}{r}} \cdot \frac{\frac{60}{d}}{\frac{60}{d}} = \frac{120}{1+\frac{60}{r}} \]
Step 3 ：Setting this expression equal to the average speed given in the graph, we find the fastest speed $r$ during the journey.
Step 4 ：\(r = \boxed{36}\) miles per hour
From Solvely APP
Solution
Step 1 ：Let $d$ denote the number of miles in the distance from the port and let $r$ denote the fastest speed of the boat (in miles per hour) on the return trip. It takes $d/60$ hours to travel from the port and $d/r$ hours to travel back to the port.
Step 2 ：Round trip, $2d$ miles are covered in $d/60+d/r$ hours for an average speed of \[ \frac{2d}{\frac{d}{60}+\frac{d}{r}} \cdot \frac{\frac{60}{d}}{\frac{60}{d}} = \frac{120}{1+\frac{60}{r}} \]
Step 3 ：Setting this expression equal to the average speed given in the graph, we find the fastest speed $r$ during the journey.
Step 4 ：\(r = \boxed{36}\) miles per hour
