Question

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?​

Answer 1

• Average speed on the paved highway is 90 km/h

• Average speed on the pasture road is 60 km/h

• Distance travelled in 1st part = 540 km

• Distance travelled in 2nd part = 180 km

Step-by-step explanation:

Given that, 720 km path is travelled in 9 hours; in which the paved highway is travelled for 6 hours and the pasture road is travelled for (9 - 6) hours = 3 hours.

Let, the average speed on the paved highway is x km/h.

Then by the given condition, the average speed on the pasture road is (x - 30) km/h

∴ in 6 hours, they travel 6x km on the paved highway and in 3 hours, they travel {3 (x - 30)} = (3x - 90) km on the pasture road.

By the given condition,

6x + (3x - 90) = 720

or, 6x + 3x - 90 = 720

or, 9x = 720 + 90 = 810

or, x = 90

∴ the average speed on the paved highway is 90 km/h

∴ the average speed on the pasture road is

= (90 - 30) km/h

= 60 km/h

∴ in the first part, for 6 hours, they travelled (6 × 90) km = 540 km and in the second part, for 3 hours, they travelled {3 (90 - 30)} km = 180 km.

Answer 2

Answer:

the average speed and the distance traveled on each part of the trip is given by:

Paved highway: Distance = 540 km

                           Speed = 90 km/h

Pasture road: Distance = 180 km

                       Speed = 60 km/h

Step-by-step explanation:

Let the distance traveled on the paved highway be x km.

The distance traveled on the pastured road is therefore = (720 - x) km

The time taken on the pastured road is = 9 - 6 = 3 hours

Now, speed = distance/time

The average speed through:

• the pasture = (720 - x)/3
• the paved highway = x/6

We have that, the average speed through the pastured road was 30 km/h less than that of the paved highway.

Writing this down we have:

(720 - x)/3 = x/6 - 30

6(720 - x) = 3x + 30 × 6 × 3

4320 - 6x = 3x - 540

9x = 4860

x = 540 km

The speed through the pasture = (720 - 540)/3 = 60 km/h

The speed through the paved highway = 540/6 = 90 km/h

The distance traveled on the paved highway = 540 km

Pasture road = 180 km