Algebra equations and explanations

Question

Two freight trucks are traveling to the same destination, and each are traveling at a constant speed. Truck A is 187187 miles away from its destination at 9 a.m., one hour after leaving from its origin, and is 9999 miles away from the destination at 10:36 a.m. Truck B started traveling to its destination at 6:30 a.m. Truck B is 248248 miles away at 8:30 a.m. and 155155 miles away at 10 a.m. Analyze each situation to determine a function that finds the distance to the destination for each truck based on the time in hours after starting the trip from the origin to the destination.

Answer 1

Draw and label diagram!

Truck A

In 1:36 (10:36 - 9:00) it traveled 88 miles (187 - 99)

Truck B

In 1:30 (10:00 - 8:30) it traveled 93 miles (248 - 155)

Now determine the rate and distance of each and convert to a function.

Answer 2

A) 88 miles in 1 hour 36 min =

88 miles in 1+36/60 hours =

88 miles in 1+3/5 hours =

88 miles in 8/5 hours

88 divided by 8/5 = 88/1*5/8 = 55 mph

B) 93 miles in 1 + 1/2 hours =

93 miles in 3/2 hours =

93 divided by 3/2 =

93*2/3 = 62 mph

The functions are D-55t and D-62t where D is the total distance one-way