Russell Carter lives on a remote ranch in the Australian outback with his dog, Spot. Several times a week he sets off with Spot for a long walk. This morning he is walking at a steady 4 mph and when they are 10 miles from home he turns to go home and, retracing his steps, lets Spot off the lead. Spot immediately runs homeward at 9 mph. When Spot reaches the ranch he turns around and runs back to Russell, who is continuing at his steady 4 mph. On reaching Russell, Spot turns back for the ranch, maintaining his 9 mph. This is repeated until Russell arrives back at the ranch and lets Spot in. At all times Russell and Spot maintain their respective speed of 4 mph and 9 mph.

How many miles does Spot cover from being let off the lead to being let into the ranch?

22.5 miles. Work out how long it takes Russell Carter to walk home. Spot has been running all this time at his constant speed so it is simple to work out how many miles Spot has covered during this period.

Russell walks for 10 miles at 4 mph, taking 2.5 hours. Spot is running for 2.5 hours too, at 9 mph, which means he covers 22.5 miles.