SOLUTION: On a journey of 100km, Jim travels at a certain speed for the first 60km, and then increases his speed by 15km/h for the remainder. If the whole journey takes 2 hours, find his two

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Question 982361: On a journey of 100km, Jim travels at a certain speed for the first 60km, and then increases his speed by 15km/h for the remainder. If the whole journey takes 2 hours, find his two speeds.
I'm in year 10, and this is an A-standard question which neither of my parents nor I could solve.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates for Travel, RT=D relates rate, time, distance.

Let r be the unknown rate for the first part;
let d be the unknown distance of the second part;

___________________rate_____________time_____________distance
part1_______________r_______________(___)_____________60
part2______________r+15_____________(___)_____________d
TOTALS_______________________________2________________100

Form expressions for the missing time quantities from the basic idea RT=D,
RT%2FR=D%2FR
highlight_green%28T=D%2FR%29


___________________rate_____________time_____________distance
part1_______________r_______________60/r______________60
part2______________r+15_____________d/(r+15)___________d
TOTALS_______________________________2________________100

Note that the distance sum arrangement will give the unknown part2 distance.
60+d=100
d=100-60
d=40
and you can adjust the tabulated information:

___________________rate_____________time_____________distance
part1_______________r_______________60/r______________60
part2______________r+15_____________40/(r+15)__________40
TOTALS_______________________________2________________100

The total time will give an equation in the single variable, r.
60%2Fr%2B40%2F%28r%2B15%29=2
This can be partly simplified to
%2860%2Fr%2B40%2F%28r%2B15%29%29%281%2F2%29=2%281%2F2%29
highlight_green%2830%2Fr%2B20%2F%28r%2B15%29=1%29

Can you solve this equation for r ?


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The algebra steps give a factorable quadratic equation, making the final answer apparent.
highlight%28highlight%28r=45%29%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

On a journey of 100km, Jim travels at a certain speed for the first 60km, and then increases his speed by 15km/h for the remainder. If the whole journey takes 2 hours, find his two speeds.
I'm in year 10, and this is an A-standard question which neither of my parents nor I could solve.
Let speed on 1st part of trip be S

Then time taken to travel 60 km = 60%2FS

On the 2nd part of trip, a 15 km/h increase in speed results in a speed of S + 15

Then time taken to travel the remaining 40 (100 - 60) km is: 40%2F%28S+%2B+15%29

Since total time was 2 hours, then we can say that:

60%2FS+%2B+40%2F%28S+%2B+15%29+=+2

60(S + 15) + 40S = 2(S)(S + 15) ------- Multiplying by LCD, S(S + 15)

60S+%2B+900+%2B+40S+=+2S%5E2+%2B+30S

100S+%2B+900+=+2S%5E2+%2B+30S

2S%5E2+%2B+30S+-+100S+-+900+=+0

2S%5E2+-+70S+-+900+=+0

2%28S%5E2+-+35S+-+450%29+=+2%280%29

S%5E2+-+35S+-+450+=+0

(S - 45)(S + 10) = 0

S, or speed on 1st part of trip = highlight_green%2845%29 km/h			OR			S = - 10 (ignore)

Speed on 2nd part of trip: 45 + 15, or highlight_green%2860%29 km/h