Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?

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Answer 1 · 2018-06-13T15:01:20

#sf(2.56color(white)(x)hr)#

or 2 hr 33 min.

At time zero Tommy sets off and after t seconds he arrives at A.

At time zero + 2hrs Zach sets off and he arrives at B at the same time as Tommy reaches A.

This means that Zach's travel time must be [t-2] hrs.

We know that distance travelled = Average speed x time taken.

So the distance travelled by Tommy = 3t

and the distance travelled by Zach = 4[t-2].

The situation looks like this:

MF Docs

Now we can apply Pythagoras:

#sf((3t)^2+[4(t-2)]^2=8^2)#

#sf(9t^2+16t^2-32t-32t+64=64)#

#sf(25t^2=64t)#

#sf(25t=64)#

#sf(t=64/25=2.56color(white)(x)hr)#