Bill is 35.0 m away from Tom. Both men walk in the same direction. Bill walks at 1.65 m/s and Tom walks at 1.85 m/s. From where they began, how far does Tom walk before he catches up with Bill? How long does it take for Tom to catch Bill?
****Please show all the steps!!!
they walk the same time t
the relative veloicty advantage Tom has is 0.20m/s
time= 35m/.2m/s= 175 seconds
tom walked=1.85m/s* 175 s= 323m
To determine how far Tom walks before he catches up with Bill, we can set up a simple equation based on their speeds and distances.
Let's define the following variables:
- Distance Bill walks = x (in meters)
- Distance Tom walks = x + 35 (since Tom starts 35 meters behind)
- Bill's speed = 1.65 m/s
- Tom's speed = 1.85 m/s
To find how long it takes for Tom to catch up with Bill, we can use the formula:
Time = Distance / Speed
So, with this in mind, we can set up the following equation:
x / 1.65 = (x + 35) / 1.85
Let's solve for x step-by-step:
1. Multiply both sides of the equation by 1.65 and 1.85 to eliminate the denominators:
1.85 * x = 1.65 * (x + 35)
After simplifying, the equation becomes:
1.85x = 1.65x + 57.75
2. Subtract 1.65x from both sides of the equation to isolate the variable x:
1.85x - 1.65x = 57.75
0.20x = 57.75
3. Divide both sides of the equation by 0.20 to solve for x:
x = 57.75 / 0.20
x = 288.75
Therefore, Tom walks approximately 288.75 meters before he catches up with Bill.
To find out how long it takes, we can substitute the value of x into either Tom or Bill's equation and solve for time:
Time = Distance / Speed
Using Bill's equation (x = distance, 1.65 m/s = speed):
Time = 288.75 / 1.65
Time ≈ 175 seconds
Therefore, it takes approximately 175 seconds for Tom to catch up with Bill.
To find out how far Tom walks before he catches up with Bill, we can set up an equation based on their respective speeds and distances:
Let's assume the time it takes for Tom to catch up with Bill is T seconds.
Distance covered by Bill = Speed of Bill * Time = 1.65 * T meters
Distance covered by Tom = Speed of Tom * Time = 1.85 * T meters
Since Bill starts 35.0 meters ahead, the equation becomes:
1.85T = 1.65T + 35.0
Now we can solve this equation to find the value of T:
1.85T - 1.65T = 35.0
0.2T = 35.0
T = 35.0 / 0.2
T = 175 seconds
So, Tom takes 175 seconds to catch up with Bill.
To find the distance Tom walks before catching up, we substitute the value of T back into one of the equations. Let's use the equation for Tom:
Distance covered by Tom = Speed of Tom * Time = 1.85 * 175 = 323.75 meters
Therefore, Tom walks 323.75 meters before he catches up with Bill.