A car passes another car on a freeway traveling 5 miles per hour faster than the slower car.?

Question

A car passes another car on a freeway traveling 5 miles per hour faster than the slower car. The faster car travels 340 miles in the time it takes the slower car to travel 315 miles. what is the speed of each car?

Not really sure on how to even start these????

Answer 1

Let s = speed of slower car

so s + 5 = speed of faster car



Recall that distance (d) that the car travels over a given period of time (t) = speed x time



So time = distance/speed



Now, the time for the slower car to travel 315 miles is 315/s (distance/slower car speed)

The time required for the faster car to travel 340 miles is 340/(s + 5)



They tell you that the cars travel their respective distance over the same period of time. So, equate these two times:



315/s = 340/(s +5)



Do some maff...



340s = 315 x (s + 5)

340s = 315s + 1575

25s = 1575

s = 63 miles per hour --> the speed of the slower car

s + 5 = 68 miles per hour --> the speed of the faster car

Answer 2

Speed of faster car is 68 m/h

Speed of slower car is 63 m/h



make an equation for both

equation for distance is distance = (speed) x (time)



315 = (speed) x (time)

340 = (speed+5) x (time)



solve for t in the first equation so t=(315/speed)



plug that answer for t into the next equation so 340 = (speed+5) x (315/speed) and now simplify/solve



340 = (speed+5) x (315/speed)

340= (315speed/speed) + (1575/speed)

340= 315 + (1575/speed)

25= 1575/speed

speed = 63



plug speed = 63 into the first and more simple equation



315 = 63 x time

time = 5



use time = 5 to check your answers...



63 is speed for slower car as you solved for speed, therefore the faster cars speed is (speed + 5) which is 68





63 x 5 = 315

68 x 5 = 340

Answer 3

velocity = distance / time

both cars took same time to travel 315 and 340 miles..

so (315 / Vslow) = (340 / Vfast)



the fast car was 5mph faster..

so Vfast = Vslow + 5



substituting this in equation 1 and solving gives

Vslow = 63mph and Vfast = 68mph