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6. A watch gains by 2% per hour when the temperature
is in the range of 40°C~50°C and it loses at the
same rate when the temperature is in the range of
20°C-30°C. However, the watch owner is fortunate
since it runs on time in all other temperature ranges.
On a sunny day, the temperature started soaring up
from 8 a.m. in the morning at the uniform rate of
2°C per hour and sometime during the afternoon it
started coming down at the same rate. Find what
time will it be by the watch at 7 pm, if at 8 am the
temperature was 32°C and at 4 pm, it was 40°C.
Answers
Given : A watch gains by 2% per hour when the temperature is in the range of 40°C~50°C
loses at the same rate when the temperature is in the range of 20°C-30°C
On a sunny day, the temperature started soaring up from 8 a.m. in the morning at the uniform rate of 2°C per hour and sometime during the afternoon it started coming down at the same rate
at 8 am the temperature was 32°C and at 4 pm, it was 40°C.
To Find : What time will it be by the watch at 7 pm, if
Solution:
at 8 am the temperature was 32°C
uniform rate of 2°C per hour
At 4 pm it was 40°C
Total Hrs = 8 hrs increased for T hrs and decreased for 8 - T hrs
=> 32 + 2T - 2(8 - T) = 40
=> 4T - 16 = 8
=> 4T = 24
=> T = 6
increased for 6 hrs and decreased for 2 hrs
Temperature after 6 hrs = 32 + 2 * 6 = 44°C
Time Temp
8 AM 32
9 AM 34
10 AM 36
11 AM 38
12 PM 40
1 PM 42
2 PM 44
3 PM 42
4 PM 40
5 PM 38
6 PM 36
7 PM 34
8 PM 32
watch gains by 2% per hour when the temperature is in the range of 40°C~50°C
12 PM to 4PM for 4hrs
watch gains 2% per hour
2% per hour = (2/100)60 = 1.2 min per hour
Gain in 4 hrs = 4 * 1.2 = 4.8 min
Time by watch at 7 pm will be 4.8 mins after 7 PM
4.8 mins = 4 Mins 48 secs
7 PM 4 Min 48 sec
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