in a week Mike ran 8km farther than Bill, while Pete ran 1 km less than 3 times as far as Bill.If pete ran 15 km farther than Mike, how many kilometers did Bill run?
thanks
To find out how many kilometers Bill ran, let's break down the information provided and solve the problem step by step.
Let's assign variables to the distances each person ran:
- Distance ran by Mike = M km
- Distance ran by Bill = B km
- Distance ran by Pete = P km
According to the given information:
1) "In a week, Mike ran 8 km farther than Bill":
M = B + 8
2) "Pete ran 1 km less than 3 times as far as Bill":
P = 3B - 1
3) "Pete ran 15 km farther than Mike":
P = M + 15
Now, we can set up equations using the above information and solve them:
B + 8 = M (Equation 1)
P = 3B - 1 (Equation 2)
P = M + 15 (Equation 3)
Since both Equation 2 and Equation 3 are equal to P, we can set them equal to each other:
3B - 1 = M + 15
Now, let's substitute the value of M from Equation 1 into this equation:
3B - 1 = B + 8 + 15
3B - 1 = B + 23
Next, we can solve for B:
3B - B = 23 + 1
2B = 24
B = 12
Therefore, Bill ran 12 kilometers.
M=B+8
P+1=3B
P-15=M
put them in standard form..
M-B=8
P-3B=-1
P-M=15
Subtract the last from the middle..
-3B+M=-16
Now subtract the first equation.
-2B=-24
B=12
check me. If correct, then finish up the others.
In a week Mike ran 8 km farther than Bill, while Pete ran 1 km less than 3 times as far as Bill.
If Pete ran 15 km farther than Mike, how many kilometers did Bill run?
Let m be how far Mike ran in km.
Let b be how far Bill ran in km.
Let p be how far Pete ran in km.
The given information is (1), (2), and (3).
(1) m = 8+b
(2) p = 3b – 1
(3) p = 15+m Use (1) to replace m in (3)
(4) p = 15+8+b Use (2) to replace p in (4)
(5) 3b – 1 = 15+8+b Subtract b from both sides. Add 1 to both sides.
(6) 2b = 24 Divide both sides by 2
(7) b = 12
Bill ran 12 km.