distance and time

Question

Mr. and Mrs. Rivers left their house at 10:00 a.m. driving in opposite directions. Mr. Rivers drove at an average speed of 48 mph and Mrs. Rivers drove at an average speed of 36 mph. 

At what time will Mr. Rivers be 24 miles farther from home than Mrs. Rivers?

Answer 1

Let's call Mr. Rivers' distance from home as a function of time a(t), and Mrs. Rivers' distance b(t).

Distance is speed multiplied by time, so we can write these equations with t as our variable for time:

a(t) = 48t

b(t) = 36t b(t) does not include a negative sign since we are talking about distance, not position

We can find when Mr. Rivers is 24 miles farther from home than Mrs. Rivers by solving this equation for t:

a(t) = 24 + b(t)

48t = 24 + 36t

12t = 24

t = 2 hours

Final answer:

2 hours after 10 am is 12pm