Question

Show an equation and solution for the problem. Jasmine and Keyla live in the same town. At 8:00 a.m. Jasmine drives west at 60 mph and two hours later Keyla drives east averaging 65 mph. How many hours after Jasmine leaves will they be 650 miles apart?

Answer 1

We could say time, t = 0 is the starting time.

We know the rates at which driver is driving. Jasmine is driving at a rate of 60 mph. Thus her distance traveled is 60t.

J = 60t

Keyla's rate is 65 miles per hour so her distance traveled is 65t. But she started two hours later so we would write 65(t - 2). We write t - 2 because at time = 2 hours, that corresponds to a distance of 65(2 - 2) = 0, which is Keyla's starting distance. Keyla starts at t = 2, but her distance is 0.

K = 65(t - 2)

Now because they are driving in opposite directions, reverse the sign for Jasmine's distance to indicate that she is driving west.

J = -60t
K = 65(t - 2)

To find out the difference in their distances we would take |J - K| or just K - J, whichever you choose.

K - J = 65(t - 2) - (-60t) = 125t - 130

Now set this distance to 250 miles

125t - 130 = 250

Solve for time, t, and this is the solution.

Answer 2

The question asked how long till they are 650 miles apart, so the distance we set it to needs to be 650, not 250. Otherwise, the solution plan is correct. To continue \[125t−130=650⟹t=\frac{780}{ 125} ≈6.24 ~hours \]

Answer 3

Between six hours fourteen minutes, and six hours fifteen minutes.

Answer 4

Thank you guys so much