a. 18 km

b. 20 km

c. 27 km

d. 35 km

**Answer:** a. 18 km

**Explanation:**

D = S x T

∴ S = | D | ; T = | D |

T | S |

Let distance be D

With speed 30km/hr he is 20 minutes (one-third of an hour) late

With speed 45 km/hr he is 8 minutes late

∴ Difference between two times = 20-8 = 12 min = | 12 | hours |

60 |

Tip:

Difference between two given times can also be easily measured or checked by looking at a watch or imagining a watch.

Also, time = T = | D |

S |

∴ | D | - | D | = | 12 |

30 | 45 | 60 |

a. 25.71 km/hr

b. 27 km/hr

c. 27.39 km/hr

d. 31.5km/hr

**Answer:** a. 25.71 km/hr

**Explanation:**

D = S x T

∴ S = | D | ; T = | D |

T | S |

Speed = S = | D |

T |

Average Speed = | Total distance travelled |

Total time taken |

Total distance travelled = D+D = 2D

The bus runs 27 kmph faster, so its speed is 45 kmph.

Total Time = t1+t2 = | d1 | + | d2 | = | D | + | D |

s1 | s2 | 18 | 45 |

∴ Average speed = | 2D | = 25.71 km/hr |

D/18 + D/45 |

a. 13 km/hr

b. 14.25 km/hr

c. 18 km/hr

d. 16.75 km/hr

**Answer:** a. 13 km/hr

**Explanation:**

D = S x T

∴ S = | D | ; T = | D |

T | S |

Speed = S = | D |

T |

Average Speed = | Total distance travelled |

Total time taken |

Total Time = t1+t2+t3 = | d1 | + | d2 | + | d3 | = | 96 | + | 124 | + | 105 | = 25 hours |

s1 | s2 | s3 | 16 | 31 | 7 |

∴ Average speed = | 325 | = 13 km/hr |

25 |

a. 22.85 km/hr

b. 25.15 km/hr

c. 40 km/hr

d. 50 km/hr

**Answer:** a. 22.85 km/hr

**Explanation:**

D = S x T

∴ S = | D | ; T = | D |

T | S |

Speed = S = | D |

T |

Average Speed = | Total distance travelled |

Total time taken |

Parts of the distance = | D | ; | D | ; remaining distance. |

4 | 4 |

Remaining distance = D - ( | D | + | D | ) = | D |

4 | 4 | 2 |

Total Time = t1+t2+t3 = | D | + | D | + | D | = | D | + | D | + | D | = | 7D |

4 x 20 | 4 x 10 | 2 x 80 | 80 | 40 | 160 | 160 |

∴ Average speed = | D | = 22.85 km/hr |

7D/160 |

a. 15 km/hr

b. 18 km/hr

c. 21 km/hr

d. 30 km/hr

**Answer:** d. 30 km/hr

**Explanation:**

D = S x T

∴ S = | D | ; T = | D |

T | S |

Distance is same

∴ D = D

∴ S1 x T1 = S2 x T2

∴ 40 x | 6 | = ? x | 8 | ---------> To convert minutes to hours, divide minutes by 60 |

60 | 60 |