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### Course: Algebra 1>Unit 3

Lesson 3: Word problems with multiple units

# Using units to solve problems: Road trip

In word problems that involve multiple quantities, we can use the units of the quantities to guide our solution. In this video, we find the cost of fuel for a road trip, using information that involves many different quantities, not all of which are useful for our problem. Created by Sal Khan.

## Want to join the conversation?

• Feel like I missed something between this section and the equations & inequalities. All of a sudden these problems are just over my head. I was cruising up until now.
• This is just an example. You should calm down, revise this, rewatch videos.
• The questions in the test after this are quite harry, and I believe more practice in the video would have provided a better understanding of the equations to follow since i am getting a 50% I seem to be missing some info... I came back to no avail. please put 3-5 practice questions in a video so those of us who get confuesed easily will be able to comprehend such harry units of measurement.
• What if there is wind or other forces helping the 🚙 move forward
• How much would it change if it cost o.75 dollars per liter?
• You would still use 20 liters of gas, (shown in ), because the distance and speed do not change. However; you'd be spending more per liter, and therefore the price would increase from 12 dollars to 15 dollars for 20 liters of gas.
• How are there 1000 cubic cm per liter? Yes centiMETERS. How?
Shouldn’t it be
1L = 100cL
(1 vote)
• A liter is a measure of volume, but think of the volume of a cube, V=l*w*h, so cubic length units create a volume. A liter was originally defined as a kg of water under certain conditions, but then redefined as 1 liter = 1000 cm^3. So this is by definition, and your second statement is also true.
• On one of the review questions similar to the road trip video I calculate that the person did not have enough fuel for the entire trip and so used all of her liters in the tank, so could not complete the trip. Your hints show the answer based on the full trip and there is no mention of refueling. Should I assume that she stopped and refueled? If so the amount given is correct, but if she only had the 20 liters of fuel she fell short of her goal, and I based my incorrect answer on that. But I probably overlooked something, which I have done several times before. Thanks for the videos and tests. You guys are great.
• 100/5=20 and 20*0.06= \$12, the answer. Jeez, if this problem is at all accurate, inflation has done a number on things...
• At , Sal said (5 km per liter) is (1/5 liter per km) and he mentioned "reciprocal".

Why is (5 km per liter) === (1/5 liter per km) ?
(1 vote)
• The definition of reciprocal is that
if 𝑎⋅𝑏 = 1, then 𝑎 and 𝑏 are each other's reciprocal.

With 𝑝, 𝑞 ≠ 0 we have
(𝑝 ∕ 𝑞)⋅(𝑞 ∕ 𝑝) = 𝑝𝑞 ∕ (𝑝𝑞) = 1
which shows that 𝑞 ∕ 𝑝 is the reciprocal of 𝑝 ∕ 𝑞.

Let 𝑝 = 5 kilometers and 𝑞 = 1 liter

We can then write 5 kilometers per liter = 𝑝 ∕ 𝑞

Thereby, the reciprocal of 5 kilometers per liter is
𝑞 ∕ 𝑝 = 1 liter ∕ (5 kilometers) = 1/5 liter per kilometer.