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Question: A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.

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

Distance: 140 km

Initial speed: 28 km/hr

Step-by-step explanation:

D = speed × time

let S be the Intial speed

And D be the half distance

D = S × 2½

D = (S + 2) × 2⅓

(5/2)S = (S + 2) × 7/3

7/3 S - 5/2 S = 14/3

S/6 = 14/3

S = 28 km/hr

D = 5×28/2 = 70

Total distance = 2×70 = 140 km

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