Page 147 - Maths Skills - 8
P. 147

Direct and Inverse Proportions                                                                         145


              Let’s Attempt


        Example 1:  Convert
                       (i)  36 km/h into m/s                          (ii)  35 m/s into km/h

                                         5                                            18
        Solution:      (i)   1 km/h =   18  m/s                      (ii)   1 m/s =    5   km/h

                                              5                                            18
                            \ 36 km/h = 36 ×     m/s = 10 m/s.             \ 35 m/s = 35 ×     km/h = 126 km/h.
                                              18                                            5

        Example 2:  A person covers a certain distance in 3 hours 15 minutes with a speed of 8 km/h. If he covers the
                       same distance on bicycle at the rate of 13 km/h, find the time taken by him.

                                                     13
        Solution:      Time taken = 3 hours 15 min =     hours, Speed of walking  = 8 km/h
                                                      4
                                                           13
                       \  Distance = (Speed × Time) =   8 ×  4    km = 26 km.


                       Now, the speed of the bicycle = 13 km/h
                                        Distance      26 km
                       \  Time taken =            =           = 2 hours
                                          Speed      13 km/h

                       Hence, on bicycle the person can cover the same distance in 2 hours.

        Example 3:  If a car covers a distance of 10.8 km in 6 hours, find the distance covered by the car in 10 hours.
                                Distance    10.8 km
        Solution:      Speed =            =           = 1.8 km/h
                                 Time       6 hours
                       Hence, the distance covered in 10 hours = (speed × time) = (1.8 km/h × 10 h) = 18 km.

        Example 4:  A motor covers a distance of 252 km in 7 hours. Find the speed of the motor and convert it into m/s.

        Solution:      Distance = 252 km                    Time = 7 hours

                                Distance    252 km
                       Speed =            =           = 36 km/h
                                 Time       7 hours
                                     5
                         1 km/h =      m/s
                                    18
                                           5
                       \  36 km/h = 36 ×      m/s = 10 m/s.
                                          18
        Example 5:  Hrithik goes to school at the rate of 4 km/h and reaches 9 minutes late. If he goes by a rickshaw at
                       the speed of 5 km/h, he reaches 6 minutes early. What is his distance to school?

        Solution:      Let the distance to the school be x km.
                       Time taken to cover x km at a rate of 4 km/h
                              Distance     x km       x           x
                          =            =            =   hour(s) =   × 60 minutes = 15x minutes
                               Speed      4 km/h     4            4
                                                                     Distance      x km
                       Time taken to cover x km at a rate of 5 km/h =    Speed   =   5 km/h
                             x         x
                          =  5  hours =   × 60 minutes = 12x minutes
                                       5
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