SOLUTION: A car travels 330 miles in 6 hours. It travels at 50 mph for the first two hours and travels the last 180 miles at 60 miles per hour. It travels at constant speed for the remaining

Question 265146: A car travels 330 miles in 6 hours. It travels at 50 mph for the first two hours and travels the last 180 miles at 60 miles per hour. It travels at constant speed for the remaining time.

Let x be the time traveled at the unknown constant speed.
The total itme for the trip was 6 hours so:
6 = time traveled at 50 mph + time traveled at 60 mph + time traveled at x mph.

(a) How long did it take to travel the first 150 miles? (hours)
(b) Where was the car after 3 hours? (miles from the start)

I thought the answer would be 100 (first two hours) plus 5/6 (50 min/60 min) since the second speed is traveling 60 miles, but we only want 50 of them, so the total would be 2+5/6 hours; but that wasn't right.
For the second part I thought it would be 100+60=160 for the first 2 hours (100 miles) + one more hour of 60mph, which would add 60. This wasn't right either.
Any help would be great I'm really confused! Thanks!
Found 3 solutions by palanisamy, stanbon, dabanfield:
Answer by palanisamy(496)   (Show Source): You can put this solution on YOUR website!
x..................x........x..........................x
A 100 B 50 C 180 D
Given, A car travels 330 miles in 6 hours.
total time = 330 miles.
total distance = 6 hours
It travels at 50 mph for the first two hours.
The ditanced in the first 2 hours = 2*50 = 100 miles.
It travels the last 180 miles at 60 miles per hour.
The time taken = 180/60 = 3 hours.
Distance travelled = 180 miles.
The balance time = 6-2-3 = 1 hour
The balance distance = 330-100-180 = 50 miles
It travels at constant speed for the remaining time.
a) Time taken by the car to travel the first 100 miles = 2 hours
Time taken by the car to travel the next 50 miles = 1 hours
So the time taken by the car to travel the first 150 miles = 2+1 = 3 hours
b) The car was at a distance of 150 miles from the starting point after 3 hours.

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A car travels 330 miles in 6 hours. It travels at 50 mph for the first two hours and travels the last 180 miles at 60 miles per hour. It travels at constant speed for the remaining time.
(a) How long did it take to travel the first 150 miles? (hours)
time = distance/rate = 150/50 = 3 hrs
-----------------------------------------------
(b) Where was the car after 3 hours? (miles from the start)
distance = rate*time = 50*3 = 150 miles
==============================================
Cheers,
Stan H.
Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website!
A car travels 330 miles in 6 hours. It travels at 50 mph for the first two hours and travels the last 180 miles at 60 miles per hour. It travels at constant speed for the remaining time.

(a) How long did it take to travel the first 150 miles? (hours)
(b) Where was the car after 3 hours? (miles from the start)

Let x be the time traveled at the unknown constant speed.
The total time for the trip was 6 hours so:
6 = time traveled at 50 mph + time traveled at 60 mph + time traveled at x mph.
The time traveled at 50 mph was 2 hours and the time traveled at 60 mph was 180/60 = 3 hours.
So the time traveled at x mph is 6 - 2 - 3 = 1 hour.
The distance traveled at x mph is 330 - 100 - 180 = 50 miles
So the car traveled 50 miles in the remaining one hour so its speed was 50 mph.
So for the first 3 hours the car traveled 50 mph or 50*3 = 150 miles.

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