Question

Driver A and B have two different routes. Driver A's route is 80km, and driver B's route is 100km. Driver B travels 10km/h faster than driver A and finishes 10 minutes earlier. What are the speeds of each driver?

Answer 1

Answer:

30 km/h , 40 km/h

Step-by-step explanation:

Let "v" is speed of driver B , then speed of driver A is (v+10)

10 min. = (1/6) hour

(80 / v) - (100/(v+10)) = 1/6

$\frac{80v+800-100v}{v^2+10v}$ = $\frac{1}{6}$

$\frac{800-20v}{v^2+10v}$ = $\frac{1}{6}$

after cross multiplication

$v^{2}$ + 10v = 4800 - 120v

v^2 + 130v - 4800 = 0

discriminant D = (130)^2 - 4 * (- 4800) = 36100

$v_{1}$ = (-130 + 190) / 2 = 30

$v_{2}$ = (- 130 - 190) / 2 is negative, not a solution.

A's speed is 30 km/h

B's speed is 40 km/h

Answer 2

Given :  Driver A's route is 80km, and driver B's route is 100km. Driver B travels 10km/h faster than driver A and finishes 10 minutes earlier

To find : speeds of each driver

Solution:

Formula Used Distance = Speed * time

Driver A Distance  = 80 km

Let say Driver A Speed = A km/Hr

Time taken by Driver A = 80/A   hr

Driver B Distance = 100 km

Driver B Speed  = A + 10 km/hr

Time taken by Driver B = 100/(A + 10)  hr

Reached 10 min earlier = 10/60 = 1/6 hr

100/(A + 10)  = 80/A   - 1/6

=> 600A = 480(A + 10) - A(A + 10)

=> 600A = 480A + 4800 - A² - 10A

=> A²  +130A - 4800 = 0

=> A² + 160A - 30A - 4800 = 0

=> A(A + 160) - 30(A + 160) = 0

=> (A - 30)(A + 160) = 0

=> A  = 30     as speed can not be - ve

Driver A Speed = 30 km/hr

Driver B Speed = 40 km/hr

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