Respuesta :
Answer:
30 miles
Step-by-step explanation:
Given: Drive to work in 45 min.
Bus would take to travel= 1 hr 15 min
Average rate on the bus is 16 mph slower than his driving rate.
Lets assume the average driving rate be "x" mph.
∴ Average rate of bus= [tex](x-16)\ mph[/tex]
Now converting unit of time taken to travel to work.
Remember; 1 hours= 60 minutes.
Time taken for drive to work= [tex]\frac{45\ minutes}{60\ minutes} = 0.75\ hour[/tex]
Time taken in bus to work= 1 hour and 15 minutes=[tex]60\ minutes+ 15\ minutes= 75\ minutes[/tex]
∴ Time taken in bus to work in hours= [tex]\frac{75\ minutes}{60\ minutes}= 1.25\ hours[/tex]
Considering the distance remain constant to travel for work.
Next, forming an equation to find the value of x.
As we know, [tex]distance= speed\times time[/tex]
⇒ [tex]x\times 0.75= (x-16)\times 1.25[/tex]
Using distributive property of multiplication.
⇒[tex]0.75x= 1.25x-20[/tex]
Adding both side by 20
⇒ [tex]0.75x+20= 1.25x[/tex]
Subtracting both side by 0.75x
⇒[tex]20= 0.5x[/tex]
Dividing both side by 0.5
⇒[tex]x= \frac{20}{0.5}[/tex]
∴ [tex]x= 40\ mph[/tex]
Hence the average rate for drive to work is 40mph.
Now, subtitiuting the value of x to find the distance travelled to work.
Distance travelled= [tex]40\times 0.75= 30\ miles[/tex]
Hence, distance travelled to work is 30 miles.
