A consultant traveled 7 hours to attend a meeting. The return trip took only 6 hours because the speed was 10 miles per hour faster. What was the consultant's speed each way?
Rachel earns $6000 less than twice as much as Tom. If their two incomes total $48,000, how much does each earn?
Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil?
A real estate agent received a 2% commission on the sale of a home. If the home sold for $201,000, how much was her commission?
A train leaves town A for town B, traveling at 35 mi/h. At the same time, a second train leaves town B for town A at 45 mi/h. If the two towns are 320 mi apart, how long will it take for the two trains to meet?
A common mistake is in the equation below:
Write a clear explanation of what error has been made and what could be done to avoid the mistake. (Do not solve the equation.)
A consultant traveled 7 hours to attend a meeting. The return trip took only 6 hours because the speed was 10 miles per hour faster. What was the consultant's speed each way?
Using V = D/T
D = 7Vo = 6(Vo + 10) where Vo = the spped out.
Solve for Vo.
Vb = the speed back = Vo + 10.
A train leaves town A for town B, traveling at 35 mi/h. At the same time, a second train leaves town B for town A at 45 mi/h. If the two towns are 320 mi apart, how long will it take for the two trains to meet?
You know how fast the two trains are approaching one another, V-approach.
You know how far apart they are at the start, D-apart.
Apply V = D/T again to solve for T.
To find the consultant's speed each way:
1. Let the consultant's speed for the outbound trip be Vo.
2. Since distance = speed × time, the distance traveled for the outbound trip is 7 × Vo.
3. The speed for the return trip is 10 miles per hour faster, so it is Vo + 10.
4. The distance traveled for the return trip is 6 × (Vo + 10).
5. Since the distances for the outbound and return trips are the same (the consultant traveled back and forth), we can set up the equation: 7 × Vo = 6 × (Vo + 10).
6. Solve the equation for Vo to find the consultant's speed for the outbound trip.
7. The speed for the return trip is then Vo + 10.
To find Rachel's and Tom's incomes:
1. Let Tom's income be x.
2. Rachel earns $6000 less than twice as much as Tom, so her income is 2x - $6000.
3. The total income is $48,000, so we can set up the equation: x + (2x - $6000) = $48,000.
4. Solve the equation for x to find Tom's income, and then substitute it back into the equation to find Rachel's income.
To find the time it takes for Ching to meet Phil:
1. Ching leaves San Francisco and travels toward Los Angeles at a speed of 50 mi/h.
2. Phil leaves Los Angeles an hour later and travels toward San Francisco at a speed of 60 mi/h.
3. The two cities are 380 miles apart.
4. Since they are traveling toward each other, their distances are decreasing at a combined rate of 50 mi/h + 60 mi/h = 110 mi/h.
5. Apply the formula V = D/T and solve for T to find the time it takes for them to meet.
To find the real estate agent's commission:
1. The commission is 2% of the sale price of the home.
2. The home sold for $201,000.
3. Calculate 2% of $201,000 to find the amount of the real estate agent's commission.
The common mistake in the equation provided is not distributing the 6 to both Vo and 10 in the equation 6(Vo + 10). To avoid this mistake, it is important to use the distributive property correctly when multiplying terms.
To solve for the consultant's speed each way, we can use the formula V = D/T, where V is the speed, D is the distance, and T is the time.
Let's assume that the consultant's speed going to the meeting is Vo. So, the distance traveled to the meeting would be 7 * Vo.
On the return trip, the speed is 10 miles per hour faster than the speed going to the meeting. So, the speed on the return trip would be Vo + 10.
The distance traveled on the return trip would be 6 * (Vo + 10).
We can set up the equation:
7 * Vo = 6 * (Vo + 10).
Simplifying the equation, we get:
7Vo = 6Vo + 60.
Rearranging the equation, we get:
Vo = 60.
So, the consultant's speed going to the meeting is 60 miles per hour, and the speed on the return trip is 60 + 10 = 70 miles per hour.
Therefore, the consultant's speed each way is 60 miles per hour and 70 miles per hour.