Last week Tom decided to cycle to his grandmother’s house.
On the first day, he cycled half of the distance.
On day 2, he cycled one half of the remaining distance.
On day 3, he cycled three quarters of the remaining distance.
On day 4, he cycled 10 miles.
On day 5, he cycled two thirds of the remaining distance and on the final day he cycled the remaining 5 miles.
How far is it to his grandmother’s house?
400 miles.
Working backwards, on the final day Tom cycled the remaining 5 miles.
On day 5, he started with 15 miles (cycled two thirds, leaving 5 miles).
On day 4, he started with 25 miles (cycled 10 miles).
On day 3, he started with 100 miles (cycled three quarters, leaving 25 miles).
On day 2, he started with 200 miles (cycled half, leaving 100 miles).
On day 1, he started with 400 miles (cycled half, leaving 200 miles).