Question

PLEASE I DONT HAVE MUCH TIME. Frederick headed for Lutzen at 3 kph. Later he increased his speed to 4 kph. If it was 52 kilometers to Lutzen and the total time of travel was 15 hours, how long did he travel

asked Feb 15, 2020 200k views

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Kiril Mytsykov · Answer 1 · 2020-02-21T17:59:57+0000

Since distance is equal to rate times time:

Let x= the time traveled at 3 km/h

Let y= the time traveled at 4 km/h

We can say that

3x+4y=52

Or that three (kilometers) times the time traveled at 3 kilometers an hour plus 4 (kilometers) times the time traveled at 4 kilometers an hour is equal to 52; the total distance traveled.

Likewise, we can see that:

x+y=15

Because x, the number of hours traveled at 3 km/h added to y, the time traveled at 4 km/h is equal to 15; the total time traveled.

Now, I'll solve by substitution.

x=-y+15

Substitute that into the other equation.

3(-y+15) + 4y = 52

Distribute

-3y + 45 + 4y = 52

Combine like terms

y + 45 = 52

Minus 45 from both sides

y = 7

So Fredrick traveled at 4 km/h for 7 hours.

Now, to find the other value, substitute the value of y into one of the original equations.

x + 7 = 15

Minus 7

x = 8

So

Time traveled at 4 km/h = 7 hours

Time traveled at 3 km/h = 8 hoursSince distance is equal to rate times time: