Two trucks are driving on the same highway at the same time

Two trucks are driving on the same highway at the same time. Truck 1 is 10 miles from Smithtown. Its distance from Smithtown, in miles, after x hours can be found using the expression 10 + 55x. The distance of Truck 2 from Smithtown is represented by the graph below. Exactly how many hours will pass before the two trucks are each the same distance from Smithtown?

Solution

Truck 2 passes through the point (1,80) and (3,160)

Slope of the line = (y2-y1)/(x2-x1) = (160-80)/(3-1) = 40 miles/hr

Using the slope form

y - 80 = 40(x-1)

y = 40x + 40

Hence the trucks will meet when

40x + 40 = 10 + 55x

30 = 15x

x = 2 hours

Hence the hour passed will be equal to 2