#2 Uniform Motion Question

Question

Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min?

Answer 1

32 one way then 48 mph back total time 1 hour 15 minutes= 5/4 hour

T= Time on return trip

speed times time = distance

48T + 32(5/4 - T)= distance = d

48T -32T = d - 40

d = 16T +40

48T = 32(5/4 -T) = 40-32T

80T =40

T =1/2 hour

d=16(1/2) +40 = 48 miles

divide by 2

48/2 = 24 miles from home to school

48 mph for 1/2 hour = 24 miles

32 mph for 3/4 hour = 24 miles