Question

some campers participated in a relay race. they werent allowed to run, so altogether they ended up covering 3/17 of a lap by bike, 14/17 of a lap on a pogo stick, 11/17 of a lap by scooter, 13/17 of a lap on a skateboard, and 4/17 of a lap on stilts. in total, how many laps did the campers travel?

laps

Explanation:

Step1: Add the fractions

To find the total number of laps, we need to add the fractions \(\frac{3}{17}\), \(\frac{14}{17}\), \(\frac{11}{17}\), \(\frac{13}{17}\), and \(\frac{4}{17}\). Since the denominators are the same, we can add the numerators directly.

$$ \frac{3 + 14 + 11 + 13 + 4}{17} $$

Step2: Calculate the numerator

First, calculate the sum of the numerators: \(3 + 14 + 11 + 13 + 4 = 45\). So the fraction becomes \(\frac{45}{17}\). But we can also simplify this as a mixed number or a whole number with a remainder, but in this case, we just need the total laps. Wait, actually, let's re - check the addition:
\(3+14 = 17\), \(17+11 = 28\), \(28+13 = 41\), \(41 + 4=45\). So \(\frac{45}{17}\approx2.647\)? Wait, no, maybe I made a mistake. Wait, let's add again: \(3+14 = 17\), \(17+11 = 28\), \(28+13 = 41\), \(41+4 = 45\). But \(\frac{45}{17}\) is the improper fraction. But maybe there is a miscalculation. Wait, no, the problem says "altogether they ended up covering \(\frac{3}{17}\) of a lap by bike, \(\frac{14}{17}\) of a lap on a pogo stick, \(\frac{11}{17}\) of a lap by scooter, \(\frac{13}{17}\) of a lap on a skateboard, and \(\frac{4}{17}\) of a lap on stilts". Wait, maybe I misread the fractions. Wait, \(\frac{3}{17}+\frac{14}{17}=\frac{17}{17} = 1\), \(\frac{11}{17}+\frac{13}{17}=\frac{24}{17}\), \(\frac{24}{17}+\frac{4}{17}=\frac{28}{17}\), and then \(1+\frac{28}{17}=\frac{17 + 28}{17}=\frac{45}{17}\approx2.647\). But that seems odd. Wait, maybe the problem is that the sum of the fractions is \(\frac{3 + 14+11 + 13+4}{17}=\frac{45}{17}=2\frac{11}{17}\). But maybe there is a mistake in the problem or in my addition. Wait, no, let's check the numbers again: 3,14,11,13,4. 3 + 14 = 17, 17+11 = 28, 28+13 = 41, 41+4 = 45. So the total number of laps is \(\frac{45}{17}\) or \(2\frac{11}{17}\). But maybe I made a mistake in the problem's numbers? Wait, no, the problem is as given. So the sum of the fractions is \(\frac{3 + 14+11 + 13+4}{17}=\frac{45}{17}\approx2.647\), but maybe the intended answer is \(\frac{45}{17}\) or we can write it as a mixed number. But let's do the addition correctly:

\(\frac{3}{17}+\frac{14}{17}+\frac{11}{17}+\frac{13}{17}+\frac{4}{17}=\frac{3 + 14+11 + 13+4}{17}=\frac{45}{17}=2\frac{11}{17}\)

But maybe there is a typo in the problem, but according to the given numbers, the sum of the numerators is 45, and the denominator is 17. So the total number of laps is \(\frac{45}{17}\) or approximately \(2.65\) laps. But maybe I made a mistake in addition. Wait, 3 + 14 is 17, 17+11 is 28, 28+13 is 41, 41+4 is 45. Yes, that's correct. So the total laps are \(\frac{45}{17}\) or \(2\frac{11}{17}\).

Answer:

\(\frac{45}{17}\) (or \(2\frac{11}{17}\))