Fu Da

Fu Da spent a whole day traveling. 5/8 of the journey was spent by airplane, and 1/4 of the remainder was by train. He spent 6 3/4 hours on the bus journey.

a) How long did Fu Da spend on the train journey?
b) How much longer did Fu Da spend on the airplane than on the bus?

Correct answer:

t =  2 ¹⁄₄ = 9/4 h
y =  8 ¹⁄₄ = 33/4 h

Step-by-step explanation:

$$\begin{gathered} b=6\frac{3}{4}=6+\frac{3}{4}=\frac{6\cdot 4+3}{4}=\frac{24+3}{4}=\frac{27}{4}=6.75\text{h} \\ \frac{5}{8}\cdot x+\frac{1}{4}\cdot (x-\frac{5}{8}\cdot x)+b=x \\ \frac{5}{8}\cdot x+\frac{1}{4}\cdot (x-\frac{5}{8}\cdot x)+6.75=x \\ 5/8\cdot x+1/4\cdot (x-5/8\cdot x)+6.75=x \\ 2.25x=54 \\ x=\frac{54}{2.25}=24 \\ x=24 \\ a=5/8\cdot x=5/8\cdot 24=15\text{h} \\ t=(x-a)/4=(24-15)/4=\frac{9}{4}\text{h}=2\frac{1}{4}\text{h}=2.25\text{h} \end{gathered}$$

$y=a-b=15-\frac{27}{4}=\frac{15\cdot 4}{4}-\frac{27}{4}=\frac{60}{4}-\frac{27}{4}=\frac{60-27}{4}=\frac{33}{4}=\frac{33}{4}\text{h}=8.25\text{h}$

Try another example