Question

Need a decent explanation thanks!

Answer 1

from what I read, the roads look like the picture below.

first off, we'd want to know the distance in "red", well, using the pythagorean theorem, that'd be √(127² + 47² ), which gives us around 135.4 miles.

now, the larger triangle containing the "red" line and the smaller triangle on the left-side containing the "green" line, are similar triangles by AA, so we can use proportions to get the distance from Appletown to "park and ride", because that is the distance that Irving is going to be covering at 45 mph, so that'd be like

`\cfrac{135.4}{127}~~ \approx ~~\cfrac{\textit{park and ride}}{94}\implies \cfrac{135.4* 94}{127}\approx\textit{park and ride}\implies 100.2\approx\stackrel{park~\&}{ride}`

now, we know that Irving is going to be covering that distance at 45 mph, so

`\begin{array}{ccll} miles&hour\\ \cline{1-2} 45&1\\ 100.2&h \end{array}\implies \cfrac{45}{100}\approx\cfrac{1}{h}\implies h\approx\cfrac{100}{45}\implies h\approx 2.22`

without boring you to death, that's about 2 hours and 13 minutes.

well, that means Irving, taking off at 8am, is going to arrive at "park and ride" at 10:13am roughly.

now, we know Carol is taking off at 9am, an hour later than Irving, and she'll be traveling the "green" distance up to the junction, well, we know her distance is 42 miles plus some change, let's use proportions to get the change.

`\cfrac{47}{127}=\cfrac{change}{94}\implies \cfrac{47\cdot 94}{127}=change\implies 34.8\approx change`

so for Carol to get to "park and ride" she'll be covering about 42 + 34.8 miles, and she needs to get there by 10:13am, that is, 1.22 of an hour later so she can get there at the same time Irving does.

so she needs to cover roughly 76.8 miles in 1.22 hours, let's do the fraction for that in miles over hours.

`\cfrac{76.8~miles}{1.22~hour} ~~ \approx ~~ 62.95` due to rounding we get 0.95, but should be 0.94 if we adjust the rounding, but roughly
`\cfrac{76.8~miles}{1.22~hour} ~~ \approx ~~ 62.95~(miles)/(hour)`