Marty leaves the airport in his private plane and flies due east at 186 mph. Two hours later, a jet leaves the same airport and flies due east at 434 mph. When will the jet overtake Marty's plane?
2.5
To determine when the jet will overtake Marty's plane, we need to solve for the time it takes for the jet to catch up to Marty.
Let's break down the information given:
- Marty's plane speed: 186 mph
- Jet's speed: 434 mph
- Time difference: 2 hours (the jet leaves 2 hours after Marty)
To find the time it takes for the jet to overtake Marty, we need to equate the distance traveled by the jet to the distance traveled by Marty's plane.
Now, let's calculate the distance Marty's plane travels during the 2-hour head start:
Distance = Speed × Time
Distance = 186 mph × 2 hours
Distance = 372 miles
During these 2 hours, Marty's plane has traveled 372 miles.
Since the jet is traveling at a faster speed, it will catch up to Marty at a certain point. Let's say the required time is 't' hours after the jet departs.
Now we can set up an equation to solve for 't':
Distance covered by the jet = Distance covered by Marty's plane + Distance Marty has already covered
Speed of the jet × time (t) = Speed of Marty's plane × (t + 2 hours) + 372 miles
434t = 186(t + 2) + 372
Now we can simplify and solve for 't':
434t = 186t + 372 + 372
434t - 186t = 744
248t = 744
t = 744 / 248
t = 3
Therefore, the jet will overtake Marty's plane 3 hours after the jet departs.
To summarize, the jet will catch up to Marty's plane after 3 hours of the jet's departure.