maths problem solving

Question

Jo is setting out on a motorway drive to Birmingham in her rather elderly car, which now struggles when climbing! 10% of the distance Jo drives is uphill, where she can average only 56 mph; 10% of the distance is downhill, where she can average 72 mph; she averages 63 mph on the flat. What is Jo's overall average speed for her whole journey? Rachel drove the same journey in her flashy new car with cruise control. She realises that she drove for 10% of the journey time at 56 mph, at 10% of the journey time at 72 mph, and at 63 mph for the remainder of the trip. Who travelled at the higher average speed for the whole journey?

Answer 1

56, 72, 63 mph for up, downhill and flat driving

10% up, 10% down, 80% flat

assume some total distance d=100 miles, calculate average speed for the full distance

10 miles up, 10 down 80 flat (assuming you didn't mean percent of time traveled)

d=rt r=rate of speed

t = d/r

=10/56 + 10/72 +80/63 = 1.58730158730158730... hours

or

(56+72)/2 = 128/2 = 64

.2(64)+.8(63) = 63.8 mph if you meant 10% of the time was uphill and 10% of the time was downhill

average speed over the full distance if you meant 10% of the distance was up, 10 downhill

=d/t = 100/1.5830... = exactly 63 mph

either way Jo and Rachel had the same average speed