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# On a 20 mile course, Pat bicycled at an average rate of 30

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Re: On a 20 mile course, Pat bicycled at an average rate of 30 [#permalink]
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sananoor wrote:
On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

(Distance traveled at 30 mph) + (Distance traveled at 8 mph) = 20 miles

Distance = (rate)(time)
Let t = the time (in hours) Pat spent running at 8 mph
Aside: 12 minutes = 1/5 hours

So, we get: (30 miles per hour)(1/5 hours) + (8 miles per hour)(t hours) = 20 miles
Simplify: 6 + 8t = 20
So: 8t = 14
t = 14/8 = 7/4 = 1.75 hours = 105 minutes

How many minutes did Pat take to cover the entire course?
Pat spent 12 minutes riding a bike, and 105 minutes running
TOTAL time = 12 + 105 = 117

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Re: On a 20 mile course, Pat bicycled at an average rate of 30 [#permalink]
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sananoor wrote:
On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

Pat originally biked 30 x 12/60 = 6 miles.

So it took him 14/8 = 7/4 = 1 3/4 = 1 hour and 45 minutes = 105 minutes to run the remaining 14 miles.

So, in total, Pat took 12 + 105 = 117 minutes to complete the course.

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Re: On a 20 mile course, Pat bicycled at an average rate of 30 [#permalink]
Pat speed first part= 30 mph
Distance travelled in 12 min= 6 miles

Pat speed second part= 8 mph
Distance travelled in second part= 20-6= 14 miles
Time taken in second half= 14/8= 1.75 hr

Total time= 1.75*6+12= 117 mins.

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Re: On a 20 mile course, Pat bicycled at an average rate of 30 [#permalink]
sananoor wrote:
On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

12 Minutes = 1/5 Hour

Given Speed = 30Miles/Hr and Time is 1/5 Hour

So, Distance covered is Time * Speed = 30*1/5 = 6 Miles , Distance left is 14 Miles

He covered it speed of 8 miles / hour , so time taken is 14/8 = > 7/4 1 & 3/4 Hours

Now, 3/4 Hours is 3/4*60 = 45 minutes

Thus, he ran for 60 + 45 = 105 Minutes and bicycled for 12 minutes, So total time taken in minutes is 105 + 12 = 117 , Answer must be (C)
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Re: On a 20 mile course, Pat bicycled at an average rate of 30 [#permalink]
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Re: On a 20 mile course, Pat bicycled at an average rate of 30 [#permalink]
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