SAT Math Problem Help Please?

Question

Caroline rides her horse at an average speed of 20 mph on a trail. She goes back home on the same trail at an average speed of 30 mph. What was her average speed, in mph, for the entire journey?

Please explain how you got to the answer (no choices) Thanks

Answer 1

[13]
24 mph
Let the distance be 60 miles (60 miles have been taken as the distance because it is the LCM of 20 and 30.We may solve the problem taking the distance as x mile or 1 mile or any distance of our choice but that will involve soution of fraction)
Time taken by her for going=60/20=3 hrs
Time taken for coming back=60/30=2 hrs
Average speed
=Total distance/Ttotal time
=120/5
=24 mph

Answer 2

average speed in total journey of twice the distance d of trail
= total distance / total time
= 2*d / { d/20 + d/30} mph
= 2 / {1/20 + 1/30} mph
= 2*20*30 / (30 + 20) mph
= 2*20*30 /50 mph
= 24 mph

Answer 3

You should do this problem this way.

Assuming the one way distance of the trail is X miles.

We've already the the Time#1=X/20

Time#2=x/30

So the total time of the entire journey is (x/20+x/30), and the entire distance is 2X.

The answers should be 2x/(x/20+x/30) [x is cancelled] .

Average speed is 24 miles/h

It looks hard but quite straightforward to understand.

Answer 4

Easiest way : pretend the trail is 60 miles (choose sixty because it is a multiple of 20 and 30).
On the first part, C. went 60 miles in 3 hours, then on the return trip went 60 miles in 2 hours.
Total distance: 120 miles. Total time: 5 hours.
Average speed: 120/5 = 24 mph.

Answer 5

you realize the thank you to get remainders once you do branch, stunning? it could have been an prolonged time, given which you have possibly been working with decimals and fractions for a on a similar time as. So purely a rapid assessment - in case you divide 13 by 3, then how many cases does 3 bypass into 13 flippantly? 4, stunning? So 4x3 = 12, and 13 - 12 can provide something of a million. in case you probably did the long branch, it would appear as if .__4 r a million 3)13 . -12 ------- ... a million ok. one thank you to get the respond is to discover an n that satisfies each and all the situations you're given interior the undertaking. it truly is fairly fantastically basic, on condition that there is just one condition - n/9 provides a the remainder of seven. So, in case you're taking n = 7, then n/9 = 0 r 7. ok, now, 5n = 5*7 = 35, and 35/9 = 3 r 8. So, something is 8. in case you choose a extra rigorous answer, you're able to do it like this: helpful integer n divided by 9 is comparable to an outstanding integer x with a the remainder of seven. So, n / 9 = x r 7 n = 9 * (x r 7) n = 9x + 7 5n = 5*(9x + 7) 5n = 45x + 35 5n / 9 = (45x + 35) / 9 5n / 9 = 45x / 9 + 35 / 9 5n / 9 = 5x + 35 / 9 5n / 9 = 5x + (27 + 8) / 9 5n / 9 = 5x + 27/9 + 8/9 5n / 9 = 5x + 3 + 8/9 Then, on condition that x is an integer, 5x + 3 is an integer. So, in the rest form, 5n / 9 = (5x + 3) r 8. so which you land up with the comparable answer. desire this permits!

Answer 6

Let 2d be the total distance for the entire journey, and t1 and t2 be the forward time and backward time, respectively.

her average speed
= total distance / total time
= 2d/(t1 + t2)
= 2/(t1/d + t2/d)
= 2/(1/20 + 1/30), since d/t1 = 20, d/t2 = 30
= 120/(3+2)
= 24 mph

Answer 7

25

(20 + 30) / 2 = 25

Answer 8

20+30 divided by 2
So 50/2
25.

Answer 9

distance = x

2x
------------------- = 24
x x
---- + ---
20 30


you can get the clues from sarkarta above