matt ran 1/5 mile less on monday than on tuesday. he ran 1/2 mile less on wednesday than he did on monday. he ran 7/10 mile more on friday than on wednesday. if matt ran 4/5 mile on friday, how far did he run on tuesday? stumped, please help!
You really have to write these down, one by one, and rearrange them in the order that they link to each other, to make sense of them.
When you've got too much information to take in at one time, you need to stop, write each piece down, understand each one, then link them together.
matt ran 4/5 mile on friday
F = 4/5
he ran 7/10 mile more on friday than on wednesday. OK, since we know Friday, that gets us Wed.
W = F - 7/10 = 4/5 - 7/10
he ran 1/2 mile less on wednesday than he did on monday. We know Wed., so we can get Mon.
W = M + 1/2
matt ran 1/5 mile less on monday than on tuesday. And from Monday, we finally get Tuesday.
T = M + 1/5
Now we can work back:
Friday = 4/5
Wednesday is 7/10 less than that
Monday is 1/2 more than Wednesday
Tuesday is 1/5 more than Monday.
4/5-7/8/10-7/10+1/2=6/10+1/5=8/10
on Friday Natalie ran 1/2 of a mile. If she ran farther on Saturday what is the distance she ran?
To find out how far Matt ran on Tuesday, let's go step by step.
Given:
- Matt ran 1/5 mile less on Monday than on Tuesday
- Matt ran 1/2 mile less on Wednesday than on Monday
- Matt ran 7/10 mile more on Friday than on Wednesday
- Matt ran 4/5 mile on Friday
1. Let's assign a variable to the distance Matt ran on Tuesday. Let's call it "x."
2. From the given information, we know that Matt ran 1/5 mile less on Monday than Tuesday. So, the distance Matt ran on Monday is x + 1/5.
3. We also know that Matt ran 1/2 mile less on Wednesday than on Monday. Hence, the distance Matt ran on Wednesday is (x + 1/5) - 1/2, which simplifies to x + 1/5 - 1/2.
4. It is given that Matt ran 7/10 mile more on Friday than on Wednesday. Therefore, the distance Matt ran on Friday is (x + 1/5 - 1/2) + 7/10, which simplifies to x + 1/5 - 1/2 + 7/10.
5. It is given that Matt ran 4/5 mile on Friday. So, we can set up the following equation:
x + 1/5 - 1/2 + 7/10 = 4/5
Now, let's solve the equation step by step:
x + 1/5 - 1/2 + 7/10 = 4/5
To add fractions, we need a common denominator. Here, the common denominator is 10.
Multiply each fraction by the appropriate factor to obtain a denominator of 10:
10(x + 1/5) - 10(1/2) + 10(7/10) = 10(4/5)
Simplifying:
10x + 2 - 5 + 7 = 8
Combine like terms:
10x + 4 = 8
Subtract 4 from both sides:
10x = 4
Divide by 10:
x = 4/10
Simplifying:
x = 2/5
Therefore, Matt ran 2/5 mile on Tuesday.