Taryn and Marcus drive towards Lake Murray. Taryn is faster than Marcus, how long did it take both to drive to Lake Murray?

Question

Taryn was 2 times faster than Marcus when driving toward lake Murray. In fact, taryn drove the 208 miles to lake Murray in 4 hours less than it took Marcus to drive 208 miles. How fast and long did it take each person to drive?

Answer 1

Jennifer, since Taryn was two times faster, that means she got there in half the time, right?  So, the simplest thing to do is let t = Taryn's time.  If that's the case, then Marcus' time (m) = 2t.

 

We can write that m = 2t

 

Now, Taryn's time was also 4 hours less than Marcus', so m = t+4.

 

Since m = m, then 2t = t +4, so t = 4 hrs.

 

That means that m = 8 hrs.

 

Those are our times.  If it took Marcus 8 hours to drive 208 miles, and we let s = the speed, then our equation is 8s = 208, so s = 26 mph.

 

Since Taryn's time was twice as fast, her speed was 52 mph.

 

I hope that helps!

Answer 2

Say, speed of  Marcus = x mph

Speed of Tarn.            =2x mph

Time taken by Marcus for 208 miles ,say = t hours

Time take n by Tarn for 208 miles           = t-4 hours

 

xt =208

x=208/t

 

2x(t-4)=208

2*208(t-4)/t=208

2t-8=t

t=8 hours

So, Marcus takes 8 hours

Taryn takes    4 hours.

Taryn is faster