Inverse Variation Word Problem

Question

Lily and James are doctors that do check-ups at a local clinic. Lili can do 3 more check-ups per hour. Lily does 80 check-ups while James does 70 check-ups and James is done 4 hours later. How many check-ups does Lily do per hour?

Answer 1

j represent James' rate, j + 3 represents Lily's rate

80 / j represents time James took

70 / (j + 3) represents time Lily took

80 / j = [70 / (j + 3) + 4]

80 / j = [70 + 4(j + 3)] / (j + 3)

80(j + 3) = j[70 + 4(j + 3)]

80j + 240 = 82j + 4j²

0 = 4j² + 2j - 240

0 = 2j² + j - 120

0 = (2j - 15)(j + 8)

James work for 7.5 hours