Question

tourist travels 1500 miles using two planes. The second plane averages 50 miles per hour faster than the first plane. The tourist uses the slower plane for the first 500 and the faster plane for the next 1000 miles. The total flying time is 6.5 hours. What is the speed of the first plane?

Answer 1

Answer

given,

tourist travels = 1500 miles

second plane averages 50 miles per hour faster than the first plane.

x = y + 50

The tourist uses the slower plane for the first 500 and the faster plane for the next 1000 miles.

total flying time = 6.5 hours

$\dfrac{500}{y} + \dfrac{1000}{x} = 6.5$

$\dfrac{500}{y} + \dfrac{1000}{y + 50} = 6.5$

$\dfrac{500(50 + y)+ 1000 y}{y(y + 50)} = 6.5$

$25000 + 600 y = 6.5 y^2 + 325 y$

$6.5 y^2 - 275 y - 25000 = 0$

on solving equation

y = 86.67 mile/hr

x = 86.67 + 50

x = 136.67 mile/hr