a party of hunter made a trip of 720km to a hunting lodge in 9 hours.they travelled 6 hours on a paved highway and the reminder of the time on a pasture road. If the average speed through the pasture was 30 km/h less than that on the highway, find the average speed and the distance travelled on each part of the trip?
Answers
The average speed on the paved highway is 90 km/hr and on the pasture road is 60 km/hr and the distance travelled on each part of the trip is 540 km and 180 km respectively.
Step-by-step explanation:
It is given that,
The hunters travelled 720 km in 9 hrs, of which they travelled 6 hrs on the paved highway
So, the remaining time travelled by them on the pasture road is (9 - 6) hours = 3 hours.
Let’s assume the average speed on the paved highway be “x” km/h, then the average speed on the pasture road will be “(x - 30)” km/h .
Therefore,
The distance travelled on the paved highway in 6 hrs will be = 6x km
And
The distance travelled on the pasture road in 3 hrs will be = 3(x-30) km = (3x – 90) km
Now, according to the question, we can write the eq. as,
6x + (3x - 90) = 720
⇒ 6x + 3x - 90 = 720
⇒ 9x = 720 + 90
⇒ 9x = 810
⇒ x = 90 ← the average speed on the paved highway
∴ The average speed on the pasture road is = x - 30 = (90 - 30) = 60 km/h
And,
The distance travelled on each part of the trip is:
Paved highway: 6x = 6*90 = 540 km
Pasture Highway: 3(x – 30) = 3(90 - 30) = 3 * 60 = 180 km
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