On Monday, Voltaire drove to town at 60 miles per hour. On Tuesday, he drove to town at 40 miles per hour. If the totaling traveling time for both trips was 15 hours, how far was it to town?
I know distance=(rate)(time).so I set it up like this...x=distance
X/(60)(15) + x/(40)(15)=
..but I end up getting the wrong answer...any advice on how to set up uniform motion problems dealing with ROUND TRIPS..thanks.
He traveled at 60 mph a distance of 60*hours.
He traveled at 40 mph the same distance of 40(15 hrs - time hrs). The distance is the same; therefore, set them equal.
60t = 40(15-t)
60t = 600 - 40t
100t = 600
t = 6 hrs for the 60 mph day.
15-t = 9 hours for the 40 mph day.
distance = 6 h x 60 mph = 360 miles.
distance = 9 h x 40 mph = 360 miles.
Check my work. Check my thinking.
i do believe this guy up is right...you just need to sit down and think about it step by step don't get frustrated and give up, just keep working on it and sooner or later you will get it,
Well, solving these types of problems can be a bit of a trip, can't it? But don't worry, I'm here to clown-sult you!
To set up the equation correctly, let's consider each day's round trip separately.
On Monday, the distance to town is represented by x, and since Voltaire is driving at 60 miles per hour, the time it takes him to get there is x/60. But remember, it's a round trip, so the total time spent on Monday is 2 times that, or 2x/60.
On Tuesday, the distance is still x, but this time he's driving at 40 miles per hour. So, the time it takes on Tuesday is x/40, and once again, it's a round trip, so the total time spent on Tuesday is 2x/40.
Now, since the total traveling time for both trips is given as 15 hours, we can set up the equation:
2x/60 + 2x/40 = 15
Now, let's simplify this equation a bit:
1x/30 + 1x/20 = 15
To get rid of those pesky fractions, let's find a common denominator, which is 60:
2x/60 + 3x/60 = 15
Adding the like terms, we get:
5x/60 = 15
Now, let's solve for x:
5x = 15 * 60
5x = 900
x = 900/5
x = 180
So, the distance to town is 180 miles. And that, my friend, is the clownclusion of this journey!
To solve this problem, you can break it down into two separate trips: Monday and Tuesday. Let's denote the distance to town as "d" (in miles).
1. Monday's trip:
- Speed: 60 miles per hour
- Time: Unknown (let's call it "t1")
- Distance: d
According to the formula distance = rate × time, we have:
d = 60t1
2. Tuesday's trip:
- Speed: 40 miles per hour
- Time: Unknown (let's call it "t2")
- Distance: d
Using the same formula, we have:
d = 40t2
Now, let's consider the total traveling time for both trips, which is given as 15 hours:
t1 + t2 = 15
We can use the equations we derived to solve for t1 and t2. First, let's solve for t1:
d = 60t1
t1 = d/60
Now, substitute this value for t1 into the equation t1 + t2 = 15:
(d/60) + t2 = 15
Next, let's solve for t2 by moving the known values to one side of the equation:
t2 = 15 - (d/60)
Now, substitute this value for t2 into the equation d = 40t2:
d = 40(15 - d/60)
Now, we can solve for d:
d = 600 - 40d/60
60d = 600 - 40d
100d = 600
d = 6
Therefore, the distance to town is 6 miles.
To set up the problem correctly, you need to consider the round trip and find the distances for each leg separately. Let's break down the problem step by step:
Step 1: Define the variables
Let x be the one-way distance to town.
Step 2: Calculate the time for each leg
On Monday, the time taken to drive one way is x/60 hours since Voltaire's speed is 60 mph.
On Tuesday, the time taken to drive one way is x/40 hours since Voltaire's speed is 40 mph.
Step 3: Set up the equation
The total time taken for both trips is 15 hours. Since the round trip includes two one-way trips, the equation becomes:
x/60 + x/40 = 15
Step 4: Solve the equation
To solve the equation, you need to find a common denominator for the fractions:
(2x + 3x) / (2*60) = 15
Simplifying further:
5x / 120 = 15
Cross-multiplying:
5x = 15 * 120
5x = 1800
Divide both sides by 5:
x = 1800/5
x = 360 miles
Therefore, the distance to town is 360 miles.
In summary, when setting up uniform motion problems for round trips, make sure to consider the distances and times for each leg of the trip separately. Then, use the total time equation to solve for the unknown variable.