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 = \(450\) \(\text{mph}\)
speed of Propeller plane = \(250\) \(\text{mph}\)
Distance travelled by propeller plane in 3 hours head start = \(\text{speed of propeller plane}\times\text{time}\)
= \(250\times3\) = \(750\) \(\text{miles}\)
Distance to be travelled by jet plane to overtake propeller plane = \(\text{distance between both planes}\)
\(750\) \(\text{miles}\)
Relative speed of both planes = \(\text{Speed of jet plane}-\text{speed of propeller plane}\)
\(450-250=200\) \(\text{mph}\)
Time taken by jet plane to overtake propeller plane =
\(\frac{\text{Distance between both planes}}{\text{relative speeds of planes}}\)
\(\frac{750}{200}=\frac{15}{4}\) \(\text{hours}\)
total distance travelled by plane = \(\text{Time taken by jet plane to overtake propeller plane}\times\text{speed of jet plane }\)
\(450\times\frac{15}{4}=1687.5\) \(\text{miles}\)
planes are \(1687.5\) \(\text{miles}\) far from starting point.
