anyone who answers this problem will get a 10 pts. in no time at all?

Question

a horse runs 40km per hour faster than a mule, the horse runs 360km in 3 hours less time than the mule goes 360km, find the speed of the two animals.

please show me the solution

Answer 1

Hi,

Let x = speed of the mule
x + 40 = speed of the horse

Since distance = rate x time, this can be solved as distance/rate = time. Our general equation is:

horse's time + 3 hours = mule's time

distance/rate for horse + 3 = distance/rate for mule

360/(x+40) + 3 = 360/x

To eliminate the fractions, multiply every term by x(x+40).
Then simplify.

360/(x+40) + 3 = 360/x
x(x+40)*360/(x+40) + 3x(x+40) = x(x+40)*360/x
360x + 3x² + 120x = 360x + 14400
3x² + 120x - 14400 = 0
3(x² + 40x - 4800) = 0
To solve this, use the quadratic formula.
............_____________
-40 ± √40² - 4(1)(-4800)
--------------------------------- = x
............2(1)

............___________
-40 ± √1600 + 19200
----------------------------- = x
............2

............_____
-40 ± √20800
------------------- = x
............2

-40 ± 144.22
------------------ = x
.......2

104.22
---------- = x
.....2

52.22 = x

The speed of the mule is 52.11 km.hr. <=== answer
The speed of the horse is 92.11 km.hr. <=== answer

To check this, the mule will go 360 km in 360/52.11 = 6.91 hours. The horse will go 360 km in 360/92.11 = 3.91 hours, exactly 3 hours less time.

I hope that helps (and that I don't mistakenly click Cancel like the first time I wrote this)"" :-)

Answer 2

A few people have missed the fact that the horse doesn't run for 3 hours. The horse runs for 3 hours *less than the mule*. 120 km / hr means 3 hours for the horse
80 km / hr means 4½ hours for the mule, but the difference is not 3 hours.

Try it this way:
Let m be the speed of the mule
Let m + 40 be the speed of the horse:

The time for the mule to run 360 km is:
360 / m

The time for the horse to run 360 km is:
360 / (m + 40)

And you were told that the mule takes 3 hours longer:
360 / m = 3 + 360 / (m+40)

360 / m = [ 3(m+40) + 360 ] / (m + 40)
360 (m + 40) = m [ 3m+120 + 360 ]
360m + 14400 = 3m² + 480m
3m² + 120m - 14400 = 0
m² + 40m - 4800 = 0

Using the quadratic formula:
m = -20 ± sqrt(1600 + 4(4800) ) / 2
m = -20 ± sqrt(1600 + 19200) / 2
m = -20 ± 5 sqrt( 16 + 192 )
m = -20 ± 20 sqrt( 13 )
m ≈ 52.111 km/hr

mule's speed ≈ 52.111 km / hr
mule's time ≈ 360 / 52.111 ≈ 6.9 hours

horse's speed ≈ 92.111 km / hr
horse's time ≈ 360 / 92.111 ≈ 3.9 hours

(P.S. I have a hard time believing that a horse and a mule could really sustain these speeds for 4 to 7 hours.)

Answer 3

Let x be the speed of the mule.The distance the horse and mule travelled was 360 km each,time the horse needs was 360/(x+40).the time the mule needs was 360/x. The speed of the horse and mule are x+40 and x respectively.
It is stated in the question that the time the horse needs is 3 hours less than that of the mule.
360/(x+40)=(360/x)-3
Use quadratic equation to solve for x,you will need a calculator to calculate the root of numbers. After you used the quadratic equation, you will find out that the answer is:

The speed of the horse is about 92.1 km/h(corrected to 3 significant places) while the speed of the mule is about 52.1 km/h(corrected to 3 significant places).

Answer 4

Let the speed of the mule be "x".
Therefore time taken by mule to travel 360Km will be = distance/speed = 360/x

Now,
The speed of horse = x+40
Time taken by horse to travel 360Km = (360/x) -3
Now since distance = speed X time,
360 =(x+40) X [(360/x)-3]
i.e. 360 = (x + 40) X [(360-3x)/x]
i.e. 360x = (x+40)(360-3x)
i.e. 360x = 360x -3x^2 + 14400 -120x
i.e. 3x^2+120x-14400 = 0
i.e x^2+40x-4800=0
This when solved gives x = 52.11
Hence the speed of mule is 52.11Km/Hour
and that of horse is 92.11Km/Hour

Answer 5

Let M and H be the velocities of the mule and the horse.

Then, write down mathematically waht you are given:

H = M + 40.
360/M = 360/H + 3

Where 360/H or 360/M = distance divided by velocity = time.

Plugging the first equation into the second one yields

360/M = 360/(M+40) + 3

I don't have my calculator on me, and it is very late at night (to tired to be doing this stuff by hand), so I'll leave the final calculation to you. it's just algebra to solve for M and from there to solve fro H.

Good luck.

Answer 6

As already answered; the horse goes/reaches 360 kilometers in 3 hours. Meanwhile, it takes the mule 4.5 hours reach 360 kilometers. A 3 to 2 ratio!

Answer 7

the horse runs 360km in 3 hours

so, 360/3= 120 km in 1 hour
speed of the horse=120 km/h

a horse runs 40km/h faster than a mule means
speed of the mule=120-40
...............................=80 km/h

Answer 8

H = M + 40 . . .. equation 1
distance = 360
let t = time of Mule
t - 3 = time of the horse
time = distance / rate
360 /M - 3 = 360/(M+40)
(360 - 3 M) / M = 360/(M+40)
(360 - 3 M) (M+40) = 360 M
360 M + 14400 - 3 M² - 120M = 360 M
3 M² +120M - 14280 = 0
M = 51.833 km/hr . .. rate if mule
H = 51.833 + 40 = 91.833 km/hr .. rate of horse

Answer 9

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Answer 10

120 and 80