Martin rides to Cambridge 30 miles away from home at the average rate of 10 miles per hour.He returns on a better road that is 50% longer where he can increase his rate by 100%.How much time does he save by
taking the better road on his return trip?
a. 2 1/4 minutes
b. 15 minutes
c. 45 minutes
d. 2 hours 15 minutes
e. 2 hours 45 minutes
please answer and explain
3 hours to Cambridge
45 miles at 20 mph = 2.25 hours
To answer this question, we need to calculate the time it takes for Martin to travel to Cambridge and back using each road.
First, let's calculate the time it takes for Martin to travel to Cambridge using the first road, which is 30 miles away and his speed is 10 miles per hour.
Time = Distance / Speed
Time1 = 30 miles / 10 miles per hour
Time1 = 3 hours
Now, let's calculate the time it takes for Martin to travel back home using the second road, which is 50% longer. Since the first road was 30 miles, the second road would be 30 * (1 + 0.5) = 45 miles.
Next, Martin can increase his speed by 100% on the better road. Therefore, his new speed becomes 10 miles per hour + 100% of 10 miles per hour = 20 miles per hour.
Time2 = Distance / Speed
Time2 = 45 miles / 20 miles per hour
Time2 = 2.25 hours
To find out how much time Martin saves by taking the better road on his return trip, we need to calculate the time difference between the two roads.
Time saved = Time1 - Time2
Time saved = 3 hours - 2.25 hours
Time saved = 0.75 hours
Since we want to convert the time saved into minutes, we multiply it by 60.
Time saved in minutes = 0.75 hours * 60 minutes/hour
Time saved in minutes = 45 minutes
Therefore, Martin saves 45 minutes by taking the better road on his return trip.
The correct answer is:
c. 45 minutes