Answer:
1687.5 miles
Step-by-step explanation:
Given: A jet plane traveling at 450 mph overtakes a propeller plane traveling at 250 mph that had a 3-hour head start.
To Find: How far from the starting point are the planes
Solution:
Speed of jet plane = [tex]450[/tex] [tex]\text{mph}[/tex]
speed of Propeller plane = [tex]250[/tex] [tex]\text{mph}[/tex]
Distance travelled by propeller plane in 3 hours head start = [tex]\text{speed of propeller plane}\times\text{time}[/tex]
= [tex]250\times3[/tex] = [tex]750[/tex] [tex]\text{miles}[/tex]
Distance to be travelled by jet plane to overtake propeller plane = [tex]\text{distance between both planes}[/tex]
[tex]750[/tex] [tex]\text{miles}[/tex]
Relative speed of both planes = [tex]\text{Speed of jet plane}-\text{speed of propeller plane}[/tex]
[tex]450-250=200[/tex] [tex]\text{mph}[/tex]
Time taken by jet plane to overtake propeller plane =
[tex]\frac{\text{Distance between both planes}}{\text{relative speeds of planes}}[/tex]
[tex]\frac{750}{200}=\frac{15}{4}[/tex] [tex]\text{hours}[/tex]
total distance travelled by plane = [tex]\text{Time taken by jet plane to overtake propeller plane}\times\text{speed of jet plane }[/tex]
[tex]450\times\frac{15}{4}=1687.5[/tex] [tex]\text{miles}[/tex]
planes are [tex]1687.5[/tex] [tex]\text{miles}[/tex] far from starting point.
