Question

9. Mrs Li took 12 hours to travel from Town E to Town F. If she increased her speed by 16 km/h, she could have saved 2.4 hours. a) What was her original speed? b) What was the distance from Town E to Town F? a) [3]​

Answer 1

64 km/h

Explanation:

Let's denote Mrs Li's original speed as "s" (in km/h).

We know that Mrs Li traveled from Town E to Town F in 12 hours at her original speed.

We can use the formula:

distance = speed × time

to set up an equation for the distance from Town E to Town F in terms of Mrs Li's original speed:

distance = s × 12

We also know that if Mrs Li increased her speed by 16 km/h, she could have saved 2.4 hours. This means that the time it would have taken her to travel the same distance at the faster speed is 12 − 2.4 = 9.6 hours.

Using the same formula, we can set up another equation for the distance from Town E to Town F in terms of Mrs Li's increased speed:

distance = (s + 16) × 9.6

Since Mrs Li traveled the same distance in both cases, we can equate these two expressions for distance:

s × 12 = (s + 16) × 9.6

Expanding the right side and simplifying, we get:

12s = 9.6s + 153.6

2.4s = 153.6

s = 64

Therefore, Mrs Li's original speed was 64 km/h.