Question

Timothy climbed a mountain in two days. Timothy spent a total of 14 hours climbing
the mountain. On the second day, Timothy walked at an average speed that was half
a kilometer per hour faster, but was two hours less than what Timothy walked on
the first day. If the total distance Timothy covered during the two days, was 52 kms,
how many kms per hour did Timothy walk on the second day?​

Answer 1

Given:

Timothy climbed a mountain in two days. Timothy spent a total of 14 hours climbing the mountain.  

On the second day, Timothy walked at an average speed that was half a kilometer per hour faster, but was two hours less than what Timothy walked on the first day.  

To find:

If the total distance Timothy covered during the two days, was 52 km, how many kms per hour did Timothy walk on the second day?​

Solution:

Timothy spent a total of 14 hours climbing the mountain. On the second day, Timothy walked two hours less than what Timothy walked on the first day.

Let time travelled during first day = x

Let time travelled during the second day = x - 2

Total time = 14

x + (x - 2) = 14

x = 8 hours

Therefore, Timothy walked 8 hours on the first day and (8 - 2) = 6 hours on the second day.

The total distance Timothy covered during the two days, was 52 km

we use the formula, speed = distance/time

speed × time = distance

On the second day, Timothy walked at an average speed that was half a kilometre per hour faster

s × 8 + (s + 0.5) (6) = 52

s × 8 + (s + 1/2) (6) = 52

8s + 6s + 3 = 52

14s = 49

s = 49/14 = 3.5

s = 3.5 km/hr

Thus the speed on the first day = 3.5 km/hr

Thus the speed on the second day = 3.5 + 0.5 = 4 km/hr

Therefore, Timothy walked 4 km/hr on the second day.

Answer 2

Timothy walks on the second day 4 km/hr.

Step-by-step explanation:

We are given that Timothy spent a total of 14 hours climbing  the mountain. On the second day, Timothy walked at an average speed that was half  a kilometer per hour faster but was two hours less than what Timothy walked on the first day.

The total distance Timothy covered during the two days was 52 km.

Let the time she walked on the first day be 'T' which means that the time she walked on the second day would be 'T - 2' because it is stated that on the second day she takes two hours less than what she walked on  the first day.

Now, the total time spent by Timothy on two days is 14 hours, that means;

         T + (T - 2) = 14

          2T = 14 + 2

          2T = 16

            T  =  $\frac{16}{2}$  = 8 hours.

This means that on the first day the time spent by her was 8 hours and on the second day the time spent by her was 6 hours.

Now, let the speed of her walking on the first day be 'S km/hr', so the speed of her walking on the second day would be '(S + 0.5) km/hr'.

Also, we know that: Distance = Speed $\times$ Time

So, Distance traveled by her on the first day + Distance traveled by her on the second day = Total Distance traveled by her during the two days

$(\text{S} \times 8) + ((\text{S}+0.5)\times 6)= 52 \text{ km}$

$8\text{S} + 6\text{S}+3= 52 \text{ km}$

$14\text{S} +3= 52$

$14\text{S}= 52-3$

S  =  $\frac{49}{14}$  = 3.5 km/hr

So, the km per hour Timothy walk on the second day = S + 0.5 = 3.5 + 0.5 = 4 km/hr.