Answer:
a
Explanation:
(a)
Let's call the distance that April travels from her starting point to the rest station "d". Then the distance that May travels from her starting point to the rest station is also "d". Since they both end up at the midpoint of the trail, we know that:
d + d = 15
Simplifying:
2d = 15
d = 7.5
We also know that April arrived at the rest station 40 minutes earlier than May. Since they both travelled the same distance, we can use the formula:
time = distance / speed
Let's call the time taken by April to reach the rest station "t". Then the time taken by May is:
t + 40/60 = t + 2/3
We know that April jogged at an average speed of r km/h, so:
t = d / r = 7.5 / r
May walked at an average speed that was 3 km/h less than April's jogging speed, so:
t + 2/3 = d / (r - 3) = 7.5 / (r - 3)
Now we can express t in terms of r:
7.5 / r + 2/3 = 7.5 / (r - 3)
Multiplying both sides by 3r(r - 3):
22.5(r - 3) + 2r(r - 3) = 22.5r
Expanding and simplifying:
24r - 135 = 0
(b)
To get the equation in the required form, we need to express r in terms of x, where x = r - 12. Substituting x + 12 for r in the equation above, we get:
24(x + 12) - 135 = 0
24x + 273 = 0
24x = -273
x = -273/24
Multiplying both sides by -12 and subtracting from 477, we get:
477 - 12x - 135 = 0
(c)
Substituting the value we got for x into x + 12, we get:
r = -273/24 + 12
r = 15/8
So April's average jogging speed was 15/8 km/h, or approximately 1.875 km/h.