A train travels from city a to city b and then to city

c. The distance from a to b is 120 miles and the distance from b to c is 187.5 miles. The average speed from a to b was 40 miles per hour, and the average speed from b to c was 75 mph. What was the average speed from a to c (that is for the entire trip) in miles per hour?

The distance from a to b is d1=120 miles, distance from b to c d2=187.5 miles

average speed (velocity) from a to b is v1=40 miles/hour

average speed from b to c is v2=75 miles/hour

The formula for average speed from a to c is v = (d1+d2) / (t1+t2)

We have not time and we will calculate it

t1=d1/v1 = 120/40=3 hour and t2=d2/v2=187.5/75=2.5hour

Average speed for a to c is

v = (120+187.5) / (3+2.5) = 307.5/5.5 = 55.9 ≈ 60miles/hour

Good luck!