Please help, I can’t figure it out!

Question

Keyshawn drives 300 miles in twice the time it takes Shelby to drive 240 miles. Shelbys speed is 30 mph greater then Keyshawn’s speed. What is the speed and time of each?

Answer 1

Answer 2

This can be answered by setting up a system of equations. Remember speed = distance/time. So rearranging, time = distance/speed

1) Assign variables: x = speed of Keyshawn

y=speed of Shelby

2) t(Keyshawn) = 300/x

t(Shelby) = 240/y

Since Keyshawn uses twice the time,

300/x = 2(240/y)

Cross multiply

300y=480x

y=8x/5

3) Set up second speed equation

Shelby's speed is 30 mph greater than Keyshawn's

x + 30 = y

4) Now use substitution to find x

x + 30 = y y =8x/5

x + 30 = 8x/5

5(x + 30) = 8x

5x + 150 = 8x

x = 50 mph. Keyshawn

y = x + 30 = 80 mph. Shelby

5) Now find the time using

t = distance/speed

t (Keyshawn) = 300/50 = 6 hrs

t (Shelby) = 240/80 = 3 hrs

I hope this is very helpful!