#13) Assign the variable, set upthe correctequation, and solve (This problem may

Question

#13) Assign the variable, set upthe correctequation, and solve (This problem may be done in more than one way.) Robert from Rochester plans to meet Michael from Montevideo at a restaurant located between the two cities. Assume the highway connecting the two cities is direct and the distance between the two cities is 300 miles. If they leave their towns simultaneously and arrive at the restaurant simultaneously, where Robert averages 48 mph and Michael averages 72 mph, then how far from Rochester is the restaurant? (Note: Drawing a diagram and setting up a table involving distance, rate and time may be helpful.) Monteuide

Explanation / Answer

let the distance from Rochester to restaurant = x miles

then the distance from Montevideo to restaurant will be 300 - x miles

they both arrive at same time

time taken by Robert = x / 48

time tken by Michael = (300 -x ) / 72

setting the two time equal

x / 48 = ( 300- x ) / 72

72 x = 48 ( 300 - x)

72x = 14400 - 48x

x = 120 miles

so, Rochester is 120 miles far from the restaurant

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