1. ## Linear Equations

A group of hikers is to travel x km by bus at an average speed of 48 km/h to an unknown destination. They then plan to walk back along the same route at an average speed of 4.8 km/h and to arrive back 24 hours after setting out in the bus. If they allow 2 hours for lunch and rest, how far must the bus take them?

I am unsure what to do with question, do I have to set up a simultaneous equation or...
Any help would be greatly appreciated!

2. One Formula

Distance = Rate * Time

One Realization

The DISTANCE of the out trip is the same as the distance of the return trip.

Build the two trips and make them take 22 hours total.

3. The speed of the bus is irrelevant.

You can work out the distance from the information given on the
student's return journey.

If they do not walk for 2 of the 24 hours, then for how many hours do they walk?
Then, on average, they walk 4.8 kilometers every hour,
so how many kilometers do they walk in total ?

You can work this out from the clues given.

They walk back the exact same amount of kilometers the bus takes them,
since they take the bus route in reverse.

If they are hikers, one would imagine they go the scenic route, rather than walk the road, but you can only assume the distances forward and back are equal.

A 22 hour hike is a bit much!

4. yes but the total time of the trip is 24 hours including rest. But it does not give the total time of just the walk back!

5. Gotcha!

6. So do you have any idea how to solve it?

7. Yes,
the bus travels 1km in $\frac{1}{48}$ hours.

It travels x km in $\frac{x}{48}$ hours.

The students travel 1 km in $\frac{1}{4.8}$ hours.

They travel x km in $\frac{x}{4.8}$ hours.

$\frac{x}{4.8}+\frac{x}{48}=22$