Question

Ed is planning daily walking workouts on the same distance of 12 km in the morning and in the evening. Usually he is walking at constant rate, however he planned his rate to be 1 km/h more in the morning than in the evening. Given he is willing to spend 5 hours and 24 minutes daily on these workouts, what should his morning rate be, in km/h?

Answer 1

The morning rate is 5 km/h.

Explanation:

Given : Ed is planning daily walking workouts on the same distance of 12 km in the morning and in the evening.

Usually he is walking at constant rate, however he planned his rate to be 1 km/h more in the morning than in the evening.

Given he is willing to spend 5 hours and 24 minutes daily on these workouts.

To find : What should his morning rate be, in km/h?

Solution :

Let the evening time be t hours.

Total time is 5 hours and 24 minutes

i.e,
`5+(24)/(60)=5+0.4=5.4`

The morning time = 5.4-t

`\text{Speed}=\frac{\text{Distance}}{\text{time}}`

Distance = 12 km

In morning the speed is

`s_1=(12)/(5.4-t)`

In evening the speed is

`s_2=(12)/(t)`

He planned his rate to be 1 km/h more in the morning than in the evening.

`\Rightarrow (12)/(5.4-t)=(12)/(t)+1`

`(12)/(5.4-t)=(12+t)/(t)`

`12* t=(12+t)* (5.4-t)`

`12t=12* 5.4-12t+5.4t-t^2`

`12t=64.8-6.6t-t^2`

`t^2+18.6-64.8=0`

`(t-3)(t+21.6)=0`

`t=3,t=-21.6`

Reject t=-21.6 we get t=3

So, evening time is 3 hours.

Morning time is 5.4-3=2.4 hours

Now, substitute the value in speed in the morning,

`s_1=(12)/(2.4)`

`s_1=5`

Therefore, The morning rate is 5 km/h.

Answer 2

The morning rate is 5 km/h

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