Question

A jet plane traveling at 550 mph overtakes a propeller plane traveling at 150 mph that had a 3​-hour head start. How far from the starting point are the​ planes?

Answer 1

The planes are 618.75 miles from starting point

Solution:

Let t is the travel time of the jet

Then  (t + 3) is the travel time of the propellar

When the jet overtakes the propellar, they will traveled the same distance

Distance is given as:

$Distance = speed \times time$

Distance equation for Jet

A jet plane traveling at 550 mph

$Distance\ by\ jet = 550 \times t\\\\Distance\ by\ jet = 550t$

Distance equation for propellar:

propeller plane traveling at 150 mph

$Distance\ by\ propellar = 150 \times (t+3)$

Equate both distance

$550t = 150(t+3)\\\\550t = 150t + 450\\\\550t - 150t = 450\\\\400t = 450\\\\t = \frac{450}{400}\\\\t = 1.125$

Find the distance from the starting point

$Distance = 550 \times t = 550 \times 1.125\\\\Distance = 618.75$

Thus they are 618.75 miles from starting point