Answer:
r = 28 km/hr
d = 140 km
Step-by-step explanation:
The distance between the two towns is d
We know the formula for distance is d = rt
A biker covered half the distance between two towns in 2 hr 30 min.
Changing the time to hours and calling the rate r
d/2 = r * 2 1/2
For the second part the rate is (r+2)
He covered the second half of the distance in 2 hr 20 min
Changing the time to hours 2 hrs 20 min = 2 1/3 hours
d/2 = (r+2)( 2 1/3)
Since the distances are the same, we can set the two equations equal
r * 2 1/2 = (r+2)( 2 1/3)
Changing to improper fractions
r (5/2) = (r+2) 7/3
Multiplying each side by 6 to clear the fractions
6r (5/2) = (r+2) 7/3*6
15r = (r+2) *14
Distribute
15r = 14r+28
Subtracting 14r from each side
15r-14r = 14r-14r+28
r = 28
Now we want to find the distance
d/2 = r * 2 1/2
d/2 = 28 (5/2)
Multiply each side by 2
d/2*2 = 28 (5/2)*2
d = 28 *5
d = 140
