Question 1197436
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I'll assume the part "the speed is reduced to 10 miles per hour" is supposed to be "the speed is reduced <font color=red>by</font> 10 <font color=red>kilometers</font> per hour".
This way the units match up, and a speed of 10 mph or 10 kph seems way too slow for a car.
If either of these assumptions are incorrect, then please let me know.



Let's organize what we know into a table<table border = "1" cellpadding = "5"><tr><td></td><td>Distance (km)</td><td>Rate (kph)</td><td>Time (hr)</td></tr><tr><td>A to B</td><td>400</td><td>x</td><td>400/x</td></tr><tr><td>B to A</td><td>400</td><td>x-10</td><td>400/(x-10)</td></tr></table>Distance = rate*time
time = distance/rate


The time duration 400/(x-10) is larger since the speed x-10 is smaller compared to speed x.
Subtracting the time durations will get us a 2 hour gap due to the phrasing "This caused the car to stay on the road 2 hours longer".


longerTime - shorterTime = 2 hour gap
400/(x-10) - 400/x = 2


The first equation @josgarithmetic has set up is close, but the tutor has them incorrectly swapped.


Multiply both sides by x(x-10) and get everything to one side
400/(x-10) - 400/x = 2
x(x-10)(400/(x-10) - 400/x) = 2x(x-10)
400x - 400(x-10) = 2x(x-10)
400x - 400x+4000 = 2x^2-20x
4000 = 2x^2-20x
0 = 2x^2-20x-4000
2x^2-20x-4000 = 0


Compare this to ax^2+bx+c = 0
We find that
a = 2
b = -20
c = -4000


Let's use the quadratic formula
{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(-20)+-sqrt((-20)^2-4(2)(-4000)))/(2(2))}}}


{{{x = (20+-sqrt(400+32000))/(4)}}}


{{{x = (20+-sqrt(32400))/(4)}}}


{{{x = (20+-  180)/(4)}}}


{{{x = (20+180)/(4)}}} or {{{x = (20-180)/(4)}}}


{{{x = (200)/(4)}}} or  {{{x = (-160)/(4)}}}


{{{x = 50}}} or  {{{x = -40}}}
The negative speed makes no sense, so we ignore it.


The only practical soluton is x = 50.


If x = 50, then x-10 = 50-10 = 40.


Check:
If you travel 400 km at a speed of 50 kph, then you take 400/50 = 8 hours
If you travel 400 km at a speed of 40 kph, then you take 400/40 = 10 hours
There is a 10-8 = 2 hour gap between the durations, so our answers are confirmed.


Answers: 
On the way to the destination, the speed is <font color=red>50 kph</font> 
On the return trip, the speed is <font color=red>40 kph</font> 
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