Rate x Time = Distance Question!

Question

Felicia left Rome at 8 a.m. and drove her Ferrari at 80 mph from Rome to Sorrento. She then took the boat to Capri for the day returning to Sorrento 5 hours later. On the return trip from Sorrento to Rome she averaged 60 mph and arrived in Rome at 8 p.m. How far is it from Rome to Sorrento?

Answer 1

She was gone for 12 hours. She spent 5 hours on a side trip. Therefore her time traveling to and from Rome was 7 hours. x will be time spent from Rome. y is the time spent going back to Rome.

equation number one is x+ y = 7

distance going = 80 • x

distance going back = 60 • y

These two distances are the same

equation 80 x = 60 y. Rewrite as

80 x - 60 y = 0

x + y = 7. Solve this system, multiply this equation by 60 then add the equations

80x - 60y = 0

60x + 60y = 420. Result is

140x = 420. Divide by 140

x = 3 then y = 4

80 • 3 = 240

60 • 4 = 240 the distance from Rome

Answer 2

Let's start with what we know. The distance from Rome to Sorrento is the same as from Sorrento to Rome. The rate going (80 mph) is faster than returning (60 mph). The total time in the car is 12 hours (from 8 am to 8 pm) minus 5 hours (boat trip to Capri). We can divide the 7 hours between the going and returning by saying X is the former time and 7 - X is the latter time. Now we're ready to use the distance formula. Since the going distance equals the returning distance, we can say rate times time going equals rate times time returning.

80X = 60(7 - X) = 420 - 60X

140X = 420

X = 3 hours

So 3 hours at 80 mph equals 4 hours at 60 mph. That makes the distance _________ miles.