Question

You drive due east down a perfectly straight freeway for 39 minutes at 0.8 miles per minute. Then you get off at a rest stop and have lunch, which takes 28 minutes. Then you get back on the freeway, which is still perfectly straight, and drive for another 54 minutes at 0.9 miles per minute in the same direction (east). The length of the on and off ramps, and the distance to the rest stop, are very small and should be ignored. What is your average velocity, to the nearest 0.1 mile per minute, for the entire trip?

Answer 1

v₁ = initial velocity in east direction = 0.8 miles per min

t₁ = 39 min

d₁ = distance travelled in first case in east direction = v₁ t₁ = 0.8 x 39 = 31.2 miles

v₂ = initial velocity in east direction = 0.9 miles per min

t₂ = 54 min

d₂ = distance travelled in second case in east direction = v₂ t₂ = 0.9 x 54 = 48.6 miles

D = total distance travelled = d₁ + d₂ = 31.2 + 48.6 = 79.8 miles

t = total time = t₁ + t₂ + 28 = 39 + 54 + 28 = 121 min

average velocity is given as

V = D/t

V = 79.8/121

V = 0.7 miles/min