Ed and Sue bike, jog, and swim at equal and constant rates. Ed covers 74 kilometers after biking for 2 hours, jogging for 3 hours, and swimming for 4 hours. Sue covers 91 kilometers after jogging for 2 hours, swimming for 3 hours, and biking for 4 hours. Their biking, jogging, and swimming rates are all whole numbers of kilometers per hour.

Find the sum of the squares of Ed's biking, jogging, and swimming rates.

Question

27-03-2024
Mathematics

High School

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Ed and Sue bike, jog, and swim at equal and constant rates. Ed covers 74 kilometers after biking for 2 hours, jogging for 3 hours, and swimming for 4 hours. Sue covers 91 kilometers after jogging for 2 hours, swimming for 3 hours, and biking for 4 hours. Their biking, jogging, and swimming rates are all whole numbers of kilometers per hour.

Find the sum of the squares of Ed's biking, jogging, and swimming rates.

Answer :

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Final answer:

Given the information in the problem, we can create expressions for the distances Ed and Sue traveled given their rates and times. By solving these equations, we find that the sum of the squares of Ed's biking, jogging, and swimming rates is 276.

Explanation:

Let's denote Ed's and Sue's rates for biking, jogging, and swimming as b, j, and s respectively in kilometers per hour (since they are the same for both Ed and Sue). Given that Ed covers 74 kilometers in a total of 2 hours biking, 3 hours jogging, and 4 hours swimming, we have the following equation: 2b + 3j + 4s = 74.

Sue, on the other hand, covers 91 kilometers after 2 hours jogging, 3 hours swimming, and 4 hours biking. Thus, we have: 2j + 3s + 4b = 91.

Considering that their biking, jogging and swimming rates are all whole numbers, solving these two equations simultaneously would yield b = 14, j = 8, and s = 4. Therefore, the sum of the squares of Ed's biking, jogging, and swimming rates would be: 14^2 + 8^2 + 4^2 = 196 + 64 + 16 = 276.

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