Mathematics 10 — Exercise 4.3 · Q4

Full question

T(d)=d/60 is travel time in hours for distance d km. Find the time for 180 km.

Step-by-step solution

1. Replace every x in the function by the specified input.

   $$\frac{1}{60}\times 180$$

2. Calculate this operation before combining the remaining terms.

   $$1\times 180=180$$

3. Calculate this operation before combining the remaining terms.

   $$60\times 1=60$$

4. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{180\times 1}{1\times 60}$$

5. Calculate this operation before combining the remaining terms.

   $$180\times \frac{1}{60}=3$$

6. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{1\times 180}{60\times 1}$$

7. Calculate these two products separately.

   $$\frac{180}{60}$$

8. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

   $$\mathrm{GCD}=60$$

9. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{60\times 1}{1\times 60}$$

10. Calculate these two products separately.

    $$\frac{60}{60}$$

11. Show the two divisions explicitly.

    $$\frac{\frac{60}{60}}{\frac{60}{60}}$$

12. Write the reduced fraction.

    $$\frac{1}{1}$$

13. Calculate this operation before combining the remaining terms.

    $$60\times \frac{1}{60}=1$$

14. Calculate this operation before combining the remaining terms.

    $$\frac{1}{1}=1$$

15. Calculate this operation before combining the remaining terms.

    $$3\times 1=3$$

16. Show the two divisions explicitly.

    $$\frac{\frac{180}{60}}{\frac{60}{60}}$$

17. Evaluate the numerator division.

    $$\frac{180}{60}=3$$

18. Evaluate the denominator division.

    $$\frac{60}{60}=1$$

19. Write the reduced fraction.

    $$3\times \frac{1}{1}$$

20. Calculate this operation before combining the remaining terms.

    $$\frac{1}{60}\times 180=3$$

21. The computed output is the function value at this input.

    $$3$$

Answer

The final answer is shown below.