Question

Bob is hiking down a 60-mile country trail. He could hike at 10 mph for the first two hours and then go the rest of the way at 30 mph or he could just go the whole way at 20 mph. How long would each of these options take? Which option is the faster?

Answer 1

Time taken for option one: 10mph (2hours) + 30mph (rest of the way)
Time taken for option two: 20mph (3 hours)

Calculate the time taken by option one, 30 mph:
60=20+30x
40/30=x
4/3 =x
1+1/3=x

It would take (option 1): 2+1+1/3= 3 1/3 hours to complete
It would take (option 2): 3 hours

Therefore, option two is faster.

Hope I helped :)

Answer 2

The above diagram gives us a pictorial view of the two options.

With the first option the hiking has two stages

Stage 1

Hike for

`speed \: = 10mph`
for

`time = 2 \: hours`

The distance covered in this stage 1 can be determined using the formula,


`Speed = (distance)/(time \: taken) \\ \\ \\ \\10mph = (distance)/(2 \: h) \\ \\ \\ distane = 2 * 10 = 20miles`

Stage 2

At this stage,the remaining distance to be covered

`= 60 -20 = 40miles`

We can again calculate the time take to cover this distance using


`Speed = (distance)/(time \: taken) \\ \\ \\ 30mph = (40miles)/(time \: taken) \\ \\ \\ time \: taken \: = (40miles)/(30mph) \\ \\ \\ \\ time \: taken \: = 1 (1)/(3) hours`

The total time taken for this option


`= 2 \: hours \: + 1(1)/(3) hours = 3 (1)/(3) \: hours`

OPTION 2

For this option, the hiker goes 30mph throughout the whole journey for


`speed = (distance)/(time \: taken) \\ \\ \\ \\ \\ 30mph = (60)/(time \: taken ) \\ \\ time \: taken = (60)/(30) = 2 \: hours`

For the first option, it took the hiker 3⅓ hours but for the second option, it took him 2 hours.


`<b>Therefore the second option is faster.</b>`