Question

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?

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