Question 1

A U-Haul moving truck covered a total distance of 6223 kilometers averaging a speed of 47 km/h in slow moving traffic and 87 km/h in fast moving traffic. The journey took 89 hours. How many hours did the U-Haul moving truck spend in slow moving traffic?

Question 2

$\begin{gathered} _{}t_1\text{ will be the time the truck spendth in the slow moving traffic} \\ t_2\text{ will be the time the truck spendth in the fast moving traffic} \\ therefore,\text{ we have: }t_1\text{ + }t_2\text{ = 89 hours}-----(1) \\ Also\colon\text{ d}_1\text{ will be the distance the truck covered in the slow moving traffic} \\ \text{ d}_2\text{ will be the distance the truck covered in the slow moving traffic} \\ Therefore,t_{1\text{ = }}\text{ }\frac{d_1}{47_{}}\text{ }t_{2\text{ = }}\text{ }\frac{d_2}{87_{}}\text{ } \\ \text{ d}_{1\text{ }}=47t_{1\text{ }}\text{ }d_2=87t_{2\text{ }}\text{ } \\ \text{But d}_{1\text{ + }}d_{2\text{ }}\text{ = 6223 ---------(2)} \\ \text{ substituting the d}_{1\text{ }}andd_2\text{ value into equation (2) becomes.} \\ \text{ 47t}_{1\text{ }}+87t_2\text{ = 6223-----------------(3)} \\ \text{Solving equation (1) and (2) Simultaneously becomes:} \\ by\text{ making t}_{1\text{ }}in\text{ equation(1) the subject of the realtion, becomes} \\ t_1=89-t_2-------------------(4) \\ \text{Substituting t}_{1_{}}\text{ into equation (3) Gives us:} \\ 47(89-t_2)\text{ }+87t_2\text{ = 6223} \\ 4183\text{ - 47}t_2\text{ + }87t_2\text{ = 6223} \\ \text{ - 47}t_2\text{ + }87t_2\text{ = 6223 - 4183} \\ \text{ 40}t_2\text{ = 2040} \\ \text{ }t_2\text{ = }\frac{\text{2040}}{40} \\ \text{ }t_2\text{ = }51\text{hours} \\ \text{Substitue t}_2\text{ into equation (4)} \\ t_1=89-t_2 \\ t_1=89-51 \\ t_1\text{ = 38hours} \\ \text{Therefore, the time the truck spend in slow moving Traffic is 38hours.} \end{gathered}$

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