Question

Adrian and Brian are brothers. They leave the house on their bicycles and head to school that is a distance of 4 km away. Adrian cycles 1 km/hour faster than Brian and arrives to school 1 minute earlier. Algebraically determine the speeds of each brother

Answer 1

Brian's rate is 15 km/hr

Adrian's rate is 16 km/hr

Explanation:

Let r = Brian's rate

r + 1 = Adrian's rate

4/r = Brian's time

4/(r + 1) = Adrian's time

The difference in times is 1 min = 1/60 hr

`(4)/(r) - (4)/(r + 1) = (1)/(60)` LCD = 60r(r + 1)

4(60)(r + 1) - 4(60)r = r(r + 1)

240r + 240 - 240r =
`r^(2)` + r

`r^(2)` + r - 240 = 0

(r - 15)(r + 16) = 0

r = 15 or r = -16

Since the rate cannot be negative, Brian's rate is 15 km/hr and Adrian's rate is 16 km/hr