On skates, Ian can travel `\frac{3}{4}`of a mile in 5 minutes. On his bike, he can travel `3\ \frac{1}{2}`miles in 12 minutes. How fast, in miles per hour, can Ian travel on skates AND on his bike?

a) 9 miles/hour

b) 17.5 miles/hour

Step-by-step explanation:

The formula for speed = Distance (Miles) / Time(hours)

a) he can travel 3/4 of a mile in 5 minutes.

= 3/4 miles = 5 minutes

We convert 5 minutes to hour

= 60 minutes = 1 hour

5 minutes = x

Cross Multiply

60x = 5

x = 5/60

x = 1/12 hour

Hence, his skate speed =

3/4miles /1/12 hour

= 3/4 ÷ 1/12

= 3/4 × 12/1

= 9 miles/hour

b) On his bike, he can travel 3 1/2 miles in 12 minutes.

= 3 1/2 = 12 minutes

= 7/2 miles = 12 minutes

We convert 12 minutes to hour

= 60 minutes = 1 hour

12 minutes = x

Cross Multiply

60x = 12

x = 12/60

x = 1/5 hour

Hence, his skate speed =

7/2 miles /1/5 hour

= 7/2 ÷ 1/5

= 7/2 × 5

= 35/2 miles/hour

= 17.5 miles/hour