Solve Math Word Problem: Bickford & Shawn Speed & Times

[bushman91]

Bickford traveled twice as fast as Shawn traveled. Thus, Bickford could travel the 320 miles to the reef in only 2 hours less than it took shawn to travel the 240-miles to Jane's house. Find the rates and times of both boys.

Just having problems figuring out the formula and how to set it up.

So Shawn is x
Which would make Bickford 2x

 

[courtrigrad]

Use $$d = rt$$. So for Bickford, $$320 = 2v(t-2)$$ and for Shawn $$240 = vt$$.

 

[bushman91]

Please explain how you set that up and the what the variables represent

 

[courtrigrad]

Distance is defined as speed $$\times$$ time . Let $$v$$ be the speed of Shawn. Then $$2v$$ is the speed of Bickford. Also, let $$t$$ be the time it takes Shawn to travel to Jane's house. Using the equation $$d = vt$$ (where v is the speed) we can set up two equations with two unknowns.

Bickford's speed is $$2v$$ and his time is $$t-2$$ (two hours less time than Shawn) and he travels 320 miles. So we have $$320 = 2v(t-2)$$.

Shawn's speed is $$v$$ and his time is $$t$$ and he travels 240 miles. So we have $$240 = vt$$. Can you solve for $$v$$ and $$t$$?

 

[bushman91]

thanks for the help, I should be able to get it now