Question

On Saturday, Alan traveled North along minor roads averaging 36 mph to visit a friend. On Sunday, he traveled East along main roads averaging 60 mph to visit his mother. The trip to visit his mother was 24 miles longer and took 18 minutes less. How many miles was the trip (one-way) that Alan made on Saturday?

Answer 1

Answer: the trip (one-way) that Alan made on Saturday was 63 miles.

Step-by-step explanation:

Let x represent the distance of the trip that Alan made on Saturday.

Let t represent the time that it took Alan to make the trip on Saturday.

On Saturday, Alan traveled North along minor roads averaging 36 mph to visit a friend.

Distance = speed × time.

Therefore, distance travelled on Saturday would be

x = 36 × t = 36t

On Sunday, he traveled East along main roads averaging 60 mph to visit his mother. The trip to visit his mother was 24 miles longer and took 18 minutes(18/60 = 0.3 hours) less. This means that the distance travelled would be

x + 24 and the time spent would be t - 0.3 hours.

Distance travelled on Sunday would be

x + 24 = 60(t - 0.3)

x + 24 = 60t - 18 - - - - - - -- - - 1

Substituting x = 36t into equation 1, it becomes

36t + 24 = 60t - 18

60t - 36t = 24 + 18

24t = 42

t = 42/24 = 1.75

x = 36t = 36 × 1.75

x = 63 miles