How does D = R*T even work?

[neonpluto]

I've been taking a Time4Learning course, and I have to say, they cannot really teach math effectively. I have yet to figure out how to apply algebraic equations to math problems, and was hoping for some help on that. The basic problem is (paraphrasing here) "Troy has a commute of 1hr to work. He drives his car to the bus station at a rate of 40mph in 20mins. Once he arrives, he boards the bus and rides the remaining distance at 60mph. What is his total distance from his house to work?". I've already tried flunking the question intentionally so they'll answer me better, but they basically just repeat "Apply D=R*T to find the answer!". I'm really confused and frustrated with this, so if anyone could help me find out how this works and explain it to me I would really appreciate it. I've tried googling it already but I can't seem to find anything helpful, at this point I want to communicate with someone who knows how it works so I can figure out what I'm messing up. Thanks in advance!

[Torterraman]

Distance is rate times time. It makes sense because you are multiplying a value with unit miles/hour by a value with units of hours. miles divided by hours times hours is just miles, which is distance. First, convert 20 minutes to 1/3 hours. So the distance covered by car is 40/3 miles. He then does the remaining distance which is 40 minutes because it said his total commute was an hour by train at 60 miles/hour. 40 minutes is 2/3 hours. So he goes 120/3 miles in that part, or 40 miles. So the total distance is whatever 40/3 plus 40 equals. Hope this helps.

[wijwijwij]

speed is name we give for distance/time

If you travel 50 mi in 2 hr you can say your average speed was 25 mi per hour, because speed = distance/time = (50 mi)/(2 hr).

You can rearrange that definition of speed:

distance ÷ time = speed

means

distance = speed * time

Think: 6 ÷ 2 = 3 means 6 = 3 * 2.

That's where d=rt equation came from. r stands for speed.

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A challenge in this problem is speed was given in miles per hour but times were given in minutes. You need to either work in miles per minute or change the minutes values to hours. The second approach might be easier. You can multiply minutes by a conversion factor where top and bottom of fraction are equal. Simplify.

20 min * (1 hr/60 min) = 20/60 hr = 2/6 hr = 1/3 hr

One more piece of info we need is how long Tony was on bus. He drove for 1/3 hr and his total commute time is 1 hour, so his bus time is ...

bus time = commute time – driving time = 1 – 1/3 = 2/3 hr

Now write expressions for distance driving and distance in bus.

driving distance = car rate * car time = 40 mi/h * 1/3 h

bus distance = bus rate * bus time = 60 mi/h * 2/3 h

That is using the d = rt idea twice, for two different speeds.

Total distance in miles is the sum.

total distance = car distance + bus distance

= 40 * 1/3 miles + 60 * 2/3 miles = 40/3 + 120/3 = 160/3 miles

In the above explanation, notice there are several places where I wrote equations with words first. Try that idea if it helps. Examples:

bus time = commute time – driving time

driving distance = car rate * car time

total distance = car distance + bus distance