Two buses leave a station at the same time and travel in opposite directions. one bus travels 14 / mih faster than the other. if the two buses are 496mi apart after 4 hours, what is the rate of each bus?

Let the speed of the slower bus be equal to x miles per hour

let the speed of the faster bus be equal to x+14 miles per hour

after every hour they would be a further 2x+14 miles apart from eachother

therefore after 4 hours they would be 4 (2x+14) = 8x + 56 miles away from eachother

since we know exactly how many miles this is we can solve for x

8x + 56 = 496

8x = 440

x = 55

x + 14 = 69

therefore, the speed of the slower bus is 55 mph whereas the speed of the faster bus is 69 mph