Lori starts jogging at 5mph. One half hour later, Debbie starts jogging on the same route at 7mph. How long will it take Debbie to catch Lori?

Question

Please solve this equation with steps

Answer 1

We need to know how much time elapses before they have

jogged the same distance:   distance = rate*time ..  d = rt

 

Lori: d = 5t

 

Debbie:  d = 7(t - 0.5)

 

Note:  our speed is in mph so we need to keep the units

consistent so the 30 minutes = 1/2 hour or 0.5 hours.

Also, the time is t-0.5 because she started half an hour later

so the amount of running time is 0.5 hours less.

 

Set the two equal to each other and solve for t

 

7(t-0.5) = 5t

7t - 3.5 = 5t

2t = 3.5

t = 3.5/2 = 1.75 hours

 

.75 = 75/100 = 3/4 of an hour

(3/4)(60) = 45 minutes

 

Debbie will catch up to Lori in 1 hour and 45 minutes