Mathematics, 18.08.2019 12:30 Angelanova69134

Adiesel train left abuja and traveled toward johannesburg. a freight train left one hour later traveling 15 km/h faster in an effort to catch up it. after five hours the freight train finally caught up. what was the diesel train's average speed?

Answers: 1

Show answers

Answers

Here is the solution:

Start with the fact that both trains have made the same distance= 's'.

In physics distance is a multiplication of speed of your train = 'v' and period of time in which it was moving= 'T' (this is only true when the speed doesn't change during movement, or we talk about avarage speed like in your task).
Then:
$s= v_{D} * T_{D}$
"D" symbol refers do diesel train

Freight train moves with 15[km/h] greater speed and it travels 1 [h] shorter then:
$s = v_{F} * T_{F} = (v_{D}+15)*(T_{D}-1)$

As the distance made by both train is the same you can compare the right parts of both equations:
$v_{D} * T_{D}=v_{F} * T_{F} = (v_{D}+15)*(T_{D}-1)$

Diesel train moved 6 hours and freight train 5 hours then:
$v_{D} * 6=(v_{D}+15)*5$
$6*v_{D}=5*v_{D}+75$
$6*v_{D}-5*v_{D}=75$
$v_{D}=75$

Here is your The average diesel train speed is 75 km/h

Answer from: Quest

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

Answer from: Quest

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder: $652=5q+r$

here $q$ ("q" for quotient) is the number of brownies each of your friends get, and $r$ is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so $q=130$ and $r=2$ .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.