jmc

Question

Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. A little later Mike started to ride his bicycle toward Josh's house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many miles had Mike ridden when they met?

Accepted Answer

Because (rate)(time) = (distance), the distance Josh rode was (4/5)(2) = 8/5 of the distance that Mike rode. Let m be the number of miles that Mike had ridden when they met. Then the number of miles between their houses is 13 = m + 85m = 135m. Thus m = 5.