Brandon and shanda walk to grandma’s house at the rate of 4 mph. they ride their bicycles back home at a rate of 8 mph over the same route that they walked. it takes them one hour longer to walk than ride. how long did it take them to walk to grandma’s?

Let X be how long it takes to walk to Grandma's house.

Speed x Time = Distance and since they walked the same route back, the distance on the way there and back should be the same.

Thus Speed1*Time1=Speed2*Time2

Let Speed1 be the speed they walk at (4 mph), and Speed2 be their biking speed (8mph)

Now it takes one hour longer to walk than bike, so Time1=Time2+1

Thus we get:
4*(Time2+1)=8*Time2
4Time2+4=8Time2
4Time2=4
Time2 equals 1 hour
Because we are trying to solve for how to get to the Grandma's house by walking, we solve for Time1=Time2+1=1+1=2 hours