A tricky Word problem on my homework

Question

Can anyone advise on how to setup these word problems...

 

1) A biker and a motor cycler left from the same location at the same time, and in the same direction. The biker went at the speed of 12mph, and the motor cycler at 40 mph. In how many hours will the distance between them more than 56 miles?

 

2) Two bikers started from a point A, riding in the same direction. The first biker rides at the speed 7 miles per hour, and the second at the speed 15 mph. However, the second biker left 4 hours after the first biker. How many hours will the second biker reach the first biker?

 

Answer 1

1) distance=rate*time

d=rt

d=12t

d+56=40t

d=40t-56

12t=40t-56

12t-40t=-56

-28t=-56

28t=56

t=2 hours

in 2 hours the biker will have traveled 2*12=24 miles

in 2 hours the cycler will have traveled 2*40=80 miles, which is 56 miles farther than the  biker

therefore the number of hours has to be greater than 2 hours for the distance between them to be greater than 56 miles

 

2) d=rt

d=7t

d=15(t-4)

7t=15(t-4)

7t=15t-60

7t-15t=-60

-8t=-60

8t=60

t=7.5 hours

check:7*7.5=52.5 miles

         15*(7.5-4)=15*3.5=52.5 miles