Algebra Distance/Speed/Time

Question

Mario’s speed on his bicycle is 6 km/hr faster than he walks. To go to the mall by bicycle takes him 12 minutes, but takes 30 minutes if he walks. How far is it to the mall?

Answer 1

D = r * 1/2

D = (r+6) * 1/5

(1/2)r = (1/5)(r+6)

5r = 2(r+6)

5r = 2r + 12

3r = 12

r = 4

walks 4 mph, for 30 minutes = 2 miles

bikes 10 mph , for 12 minutes = 2 miles

2 miles

Answer 2

1) Write down what is given to you and assign variables for bike speed and walking speed

Bike speed (B) = walking speed (W) + 6

B = W + 6

W = B - 6

** pay attention to units!! We may need to use this conversion later on:

6 km / 1 hr = 6 km / 60 minutes = 1 km / 10 minutes

2) Recall the formula that relates distance, rate and time

Distance = rate x time

Mall distance (M) = B x 12 minutes

M = W x 30 mins

3) set them equal to each other!

12B = 30W

4) substitute!

12 (W+6) = 30W

5) Solve!

12W + 72 = 30W

72 = 18W

W = 4

6) substitute again!

B = W+ 6

B = 4 + 6

B = 10

Bike speed = 10 km/hr or 10 km/60 mins or 1km/6 mins

Walking speed = 4 km/hr or 4 km/60 mins or 1km/15 mins

M = W x 30 mins

M = (1km/15mins) x 30 mins = 2 km

or

M = B x 12 mins

M = (1km/6mins) x 12 mins = 2km

7) Final answer = It is 2 km to the mall