Answer:
The morning rate is 5 km/h
Step-by-step explanation:
Let the evening time is t
∴ The morning time = total time - t
∵ Total time is 5 hours and 24 minutes = 5 + 24/60 = 5 + 2/5 = 5.4 hrs
∴ The morning time = 5.4 - t
∵ The rate = distance / time
∵ Morning distance = 12 and morning time = (5.4 - t) h
∵ Evening distance = 12 km and evening time = (t) h
∵ The morning rate = (evening rate + 1) km/h
∴ 12/(5.4 - t) = 12/(t) + 1
∴ 12/(5.4 - t) = (12 + t)/t ⇒ use cross multiplication
∴ (5.4 - t) (12 + t) = 12 × t
∴ 64.8 + 5.4t - 12t - t² = 12t
∴ 64.8 - 6.6t - t² = 12t
∴ t² + 6.6t + 12t - 64.8 = 0
∴ t² + 18.6t - 64.8 = 0
∴ (t - 3) (t + 21.6) = 0 ⇒ (t + 21.6) rejected no -ve value for time)
∴ t - 3 = 0 ⇒ t = 3 h
∵ The evening time = 3 h
∴ The morning time = 5.4 - 3 = 2.4 h
∴ The morning rate = 12/2.4 = 5 km/h
