Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanthi crossed the finish line, how far ahead of Belle was she?
What seems to be a reasonable answer for you?
I haven't been able to come up with an equation to solve this but the answers say it's 9km/h
That answer doesn't make sense to me. It doesn't answer the question -- how far ahead of Belle was she?
This is the exact question from my textbook. It is very confusing
Please check with your teacher.
I just checked the question and there is no typo. This is the exact question. Could you please help me
The answer was 250 metres though
To figure out how far ahead Shanti was from Belle when she crossed the finish line, we need to calculate the distance each of them covered in relation to Nina.
Let's say the distance covered by Nina, Shanti, and Belle is represented as n, s, and b, respectively.
We know that when Nina crossed the finish line, she was 200 m ahead of Shanti and 400 m ahead of Belle. So we can write the equations as:
n = s + 200 (Equation 1)
n = b + 400 (Equation 2)
We also know that the total distance covered by all three runners is 1000 m:
n + s + b = 1000 (Equation 3)
Now we can solve this system of equations to find the values of n, s, and b.
Substitute Equation 1 into Equation 3:
(s + 200) + s + b = 1000
2s + 200 + b = 1000
Rearrange the equation:
2s + b = 800 (Equation 4)
Substitute Equation 2 into Equation 4:
2s + (n - 400) = 800
2s + n - 400 = 800
Rearrange the equation:
2s + n = 1200 (Equation 5)
Now we have two equations: Equation 4 and Equation 5.
Subtract Equation 5 from Equation 4:
(2s + b) - (2s + n) = 800 - 1200
b - n = -400
Rearrange the equation to isolate b:
b = n - 400
Since we know that n = s + 200 from Equation 1, substitute this into the equation above:
b = s + 200 - 400
b = s - 200
So, when Shanti crossed the finish line, she was 200 meters ahead of Belle.