Cycling trip fractions

The Malíkova family plans a 120 km cycling trip for 4 days. They want to cover a quarter of the entire route on the first day. The second day, 2/15, and the third day, 7/20, will cover the entire length of the trip. What part of the trip will they cover in three days, and how many kilometers will they have left on the last day?

Final Answer:

x =  88 km
d =  32 km

Step-by-step explanation:

$$\begin{gathered} v=120\text{km} \\ a=v/4=120/4=30\text{km} \\ b=\frac{2}{15}\cdot v=\frac{2}{15}\cdot 120=\frac{2\cdot 120}{15}=\frac{240}{15}=16\text{km} \\ c=\frac{7}{20}\cdot v=\frac{7}{20}\cdot 120=\frac{7\cdot 120}{20}=\frac{840}{20}=42\text{km} \\ x=a+b+c=30+16+42=88\text{km} \end{gathered}$$

$d=v-x=120-88=32\text{km}$

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