Bob and Jack enter a 1000 km bicycle race. Bob cycles 4 km/h faster than Jack, but his bicycle gets a flat tire, which takes 30 minutes to repair. If both of them finish the race in a tie, then how fast was each boy cycling?

Question

Hailey Morgan

Mathematics

10 March, 17:41

Bob and Jack enter a 1000 km bicycle race. Bob cycles 4 km/h faster than Jack, but his bicycle gets a flat tire, which takes 30 minutes to repair. If both of them finish the race in a tie, then how fast was each boy cycling?

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Answers (1)

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Trent Harrell · Answer 1

Let Jack's speed be x. Bob's is then x + 4.

Jacks time for the 1000 km is 1000/x.

Bob's is 1000 / (x+4) + 1/2 (the 1/2 being the 30 minutes he was delayed).

They tied so their times were equal. 1000/x = 1000 / (x+4) + 1/2.

We multiply by x (x+4) and get 1000 (x+4) = 1000x + x (x+4) / 2.

Simplifying, we get x^2 + 4x - 8000 = 0. x = [ - 4 + √ (16 + 32000) ]/2 = √8004 - 2, Jack's speed.

Bob's will be √8004 + 2.

This seems way too fast! But I don't see any mistake