Its for extra credit. YES i tried it 2 times. NO my teacher won't help us. Need a little help is all for some extra credit. No worries if you dont know it.
A car starts on a 100mile trip @ 1pm and averages 35 mph over narrow side roads until it reaches the highway, where it averages 50 mph for the rest of the trip. If the entire trip takes 2.5 hours, at what time does the car reach the highway?
I thought it was impossible. I hate word problems lol
2006-09-14 12:21:07 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
distance = rate * time
100 = (35 * x) + (50 * (2.5 - x))
100 = 35x + 125 - 50x
-25 = -15 x
x = 25 / 15 = 5 / 3 hours
5 / 3 hours = 1 hour 40 minutes
If it started at 1pm, + 1 hr 40 minutes, it = 2.40pm when it hits the highway.
2006-09-14 12:23:06 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Let S be the time on the small road (in hours).
Let H be the time on the highway (in hours)
Two equations:
S + H = 2.5
35S + 50H = 100
Now solve for S:
S = 2.5 - H
Put this into the second equation:
35( 2.5 - H ) + 50H = 100
Simplify:
35( 2.5 ) - 35H + 50H = 100
87.5 + 15H = 100
Subtract 87.5 from both sides:
15H = 12.5
H = 12.5 / 15
H = 0.8333 hrs. (5/6 hours, or 50 minutes).
S = 1.6667 hrs. (1 2/3 hours, or 100 minutes).
So the car travelled 1 2/3 hours (100 minutes) at 35 mph (58 1/3 miles) on the side road. Then it travelled 5/6 hour (50 minutes) at 50 mph (41 2/3 miles). That's a total of 100 miles:
If it started at 1pm, then it reached the highway at 2:40pm.
2006-09-14 12:24:53 · answer #2 · answered by Puzzling 7 · 0⤊ 0⤋
This must be solved in terms of time which is distance divided by rate therefore:
x/35 + (100-x)/50 = 2.5
Multiplying both sides by 350 to clear fractions
10x + 700 - 7x = 875
3x + 700 = 875
3x = 175
x=58
The car travels 58 miles at 35 mph so that is 1.67 hrs which means 2:40pm
2006-09-14 12:29:14 · answer #3 · answered by MollyMAM 6 · 0⤊ 0⤋
Okay, with x being the hours spent on narrow roads, and y being hours on the highway, then 35x+50y=100, and x+y=2.5.
Then just solve those equations.
Can you solve it from there?
2006-09-14 12:31:56 · answer #4 · answered by yljacktt 5 · 0⤊ 0⤋
If some thing is 40% smaller, you basically subtract 40%. So 40% of 40 energy is sixteen: you are attempting this by utilising multiplying 40 by utilising 0.4. the respond could be 40 - sixteen = 24 A shorter way might basically be to multiply by utilising 40 by utilising 0.6, because of the fact it is a million-0.4.
2016-11-07 08:24:00 · answer #5 · answered by ? 4 · 0⤊ 0⤋
let t be the time taken for the narrow road
then the distance = 35t + 50(2.5-t) = 100
125-15t=100 and there you have it....
2006-09-14 12:25:31 · answer #6 · answered by m s 3 · 1⤊ 0⤋