motorcycle.

Question

a motorcycle traveling at 50 miles per hour overtakes a car traveling at 40 mph that had a 3 hours head start. how far from the starting point are the 2 vehicles

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to find a way to relate the two variables to one another based on the information given in the question. On this one we have

dist(motorcycle) = dist(car)

50t = 40(t + 3) because the motorcycle has been traveling at a speed of 50 miles per hour for “t” hours and the car has been traveling at a speed of 40 mph for “t + 3” hours

From there then you want to solve for the value of “t” algebraically

50t = 40t + 120

10t = 120

t = 12

that means that the motorcycle travels for 12 hours before overtaking the car.

Then to convert that over into a distance you can use the 50t expression

50 x 12 = 600 miles

So the two vehicles are 600 miles from the starting point when the motorcycle overtakes the car.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

let t be the time when both motorcycles are at the same distance from the starting point.

 

50(t -3)= 40t

 

50t - 150 = 40t

 

50t - 40t = 150

 

10t = 150

 

so t = 15

 

15 hours * 40 mph = 600 miles.