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

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) (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 ,

___________________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.

This can be partly simplified to

Can you solve this equation for r ?

---
The algebra steps give a factorable quadratic equation, making the final answer apparent.

Answer by MathTherapy(10557) (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 =
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:
Since total time was 2 hours, then we can say that:

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

(S - 45)(S + 10) = 0
S, or speed on 1st part of trip = km/h OR S = - 10 (ignore)
Speed on 2nd part of trip: 45 + 15, or km/h
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