Math Question Algebra

Question

A jogger starts from one end of a 17-mile nature trail at 8:00 A.M. One hour later, a cyclist starts from the other end of the trail and rides toward the jogger. If the rate of the jogger is 5 mph and the rate of the cyclist is 11 mph, at what time will the two meet?

Answer 1

Here's another approach:

t = time in hrs for the jogger before they meet (hrs after 8 a.m.)

In time t the jogger goes 5t mi. d_j = 5t

The cyclist starts an hr later, so his/her travel time is t - 1 and his/her distance is d_c = 11(t - 1)

d_c + d_j = 17 5t + 11(t - 1) = 17 after doing the algebra, t = 1 3/4 hr, or 9:45 a.m.

Answer 2

After an hour it will be 9:00 and the jogger has 12 miles left to go.

When they meet up,

5t = 12-11t

16t=12

t = 12/16 = 3/4 = 0:45 minutes

So they meet up at 9:45