Question

To travel 80 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 60 miles riding a bicycle. Sue travels 10 miles per hour faster than Doreen. Find the times and rates of both girls.

Answer 1

Answer:

Time taken by Doreen is 6 hours and speed is 10 miles per hour.

Time taken by Sue is 4 hours and speed is 20 miles per hour.

Step-by-step explanation:

Let the speed of Doreen be x

According to the question  speed of Sue   is = x+10

time  taken By Sue to cover 80 miles = $\frac{80}{x+10}$

time taken by Doreen to travel 60 miles = $\frac{60}{x}$

According to question Sue take two hours less than Doreen takes

therefore

$\frac{60}{x}$ - $\frac{80}{x+10}$ =2

$\frac{60(x+10)-80x}{x(x+10)}$ =2

60(x+10) -80x = 2(x(x+10)

60x+600-80x = $2x^2+20x$

simplifying it ,we get

$2x^2+40x-600=0$

Dividing both sides by 2 ,we get

$x^2+20x-300=0$

solving it for x ,we get

(x+30)(x-10) =0

x =-30 which is not possible

x =10 miles per hour

Speed of Doreen = 10 miles per hour

Speed of Sue = 10+10 = 20 miles per hour

Time taken by Doreen = 60 divided by 10 = 6 hours

Time taken  by Sue = 80 divided by 20 = 4 hours