Concepts addressed: **unit conversion**, **velocity calculation**s.

Recommended grade: **8th**.

Difficulty level: **Basic**.

An advanced version of Mountain trip is also available.

**Scenario:**

Winter break is here, and you’re planning a trip to the mountains for a few days **with three friends**. The cabin you’ll be staying in is **a hundred miles away**, so you decide to make it a road trip and go there by car:

- How long will the ride take if you travel
**at 60 mph****on average**, with**one 15 min stop**along the way (the stop doesn’t affect the average speed)? - How much will the trip cost (there and back)
**per person**if the car burns**a gallon of fuel every 25 miles**, and gas costs**$2.60 per gallon**? Include**$20 for those necessary snacks**. - When you get close to the destination, it turns out that the last
**thousand feet**are inaccessible by car, so you have to walk. Assuming that your**walking speed with your bags is, on average, 3 mph**, how long will it take for you to cover this final?**Give the result in minutes**.

**Useful calculators:**

- Speed calculator – https://www.omnicalculator.com/everyday-life/speed
- Gas calculator – https://www.omnicalculator.com/everyday-life/gas
- Conversion calculator – https://www.omnicalculator.com/conversion/conversion-calculator

**Question 1 hints:**

**Question 2 hints:**

**Question 3 hints:**

**Solutions:**

**Step-by-step solution:**

**the distance we have to travel**

**100 miles**, s = 100 mi, and we travel at 60 mph on average, v = 60 mph. Let us first use the speed calculator to compute

**how long we are driving for**:

*t_driving = s / v = 100 mi / 60 mph = 5/3 h = 1 hr 40 min*.

But that is not the time of the whole trip, since we want to make a 15 min break on the way. Therefore, the total time is*t = t_driving + 15 min = 1hr 40 min + 15 min = 1hr 55 min*.

**1 US gal of fuel per 25 mi**. Since we’ll be travelling 200 mi (since it’s 100 mi there and 100 mi back), then in total we need 200 / 25 = 8 US gal of petrol. This means that the fuel itself will cost us 8 * $2.60 = $20.80.

Now is the time to** include the snacks**. The scenario tells us that we’ll be buying $20 worth of them, which gives*total_cost = fuel_cost + snack_cost = $20.80 + $20 = 40.80*.

Lastly, just as in the gas calculator, let us divide that sum by the number of passengers, which is 4, to find how much everyone has to pay:*cost = total_cost / no_of_passengers = $40.80 / 4 = $10.20*.

**both the distance and the velocity change**this time: we are walking the last s_walk = 1000 ft of the way at 3 mph on average, v_walk = 3 mph.

Note that in our calculations, we need the units to agree, so we need to **change the distance to miles**. Let’s use the conversion calculator to get s_walk = 1000 ft = 0.1894 mi.

Now we are ready to calculate the time it will take us to walk the distance:*t_walk = s_walk / v_walk = 0.1894 mi / 3 mph ≈ 0.0631 hr*.

The scenario, however, wants us to** give this time in minutes**. We know that **one hour is 60 minutes**. Therefore,*t_walk ≈ 0.0631 hr = 0.0631 * 60 min = 3.786 min ≈ 3 min 47 sec*.

A bonus:what are you teaching next week? We'd love to prepare a scenario for you 🙂